1. Abstract

The HVT package is a collection of R functions to facilitate building topology preserving maps for rich multivariate data analysis. Tending towards a big data preponderance, a large number of rows. A collection of R functions for this typical workflow is organized below:

Data Compression: Vector quantization (VQ), HVQ (hierarchical vector quantization) using means or medians. This step compresses the rows (long data frame) using a compression objective.
Data Projection: Dimension projection of the compressed cells to 1D,2D or Interactive surface plot with the Sammons Non-linear Algorithm. This step creates topology preserving map (also called as embedding) coordinates into the desired output dimension.
Tessellation: Create cells required for object visualization using the Voronoi Tessellation method, package includes heatmap plots for hierarchical Voronoi tessellations (HVT). This step enables data insights, visualization, and interaction with the topology preserving map. Useful for semi-supervised tasks.
Scoring: Scoring new data sets and recording their assignment using the map objects from the above steps, in a sequence of maps if required.

x	y	z
-2.6282	0.5656	-0.7253
-1.4179	-0.8903	0.9455
-1.0308	1.1066	-0.8731
1.8847	0.1895	0.9944
-1.9506	-2.2507	0.2071
-1.4824	0.9229	0.9672

x	y	z
-2.6282	0.5656	-0.7253
-1.4179	-0.8903	0.9455
-1.0308	1.1066	-0.8731
1.8847	0.1895	0.9944
-1.9506	-2.2507	0.2071
-1.4824	0.9229	0.9672

3. Map A : Base Compressed Map

Let us try to visualize the compressed Map A from the flow diagram below.

Figure 1: Data Segregation with highlighted bounding box in red around compressed map A

This package can perform vector quantization using the following algorithms -

Hierarchical Vector Quantization using k−means
Hierarchical Vector Quantization using k−medoids

For more information on vector quantization, refer the following link.

The trainHVT function constructs highly compressed hierarchical Voronoi tessellations. The raw data is first scaled and this scaled data is supplied as input to the vector quantization algorithm. The vector quantization algorithm compresses the dataset until a user-defined compression percentage/rate is achieved using a parameter called quantization error which acts as a threshold and determines the compression percentage. It means that for a given user-defined compression percentage we get the ‘n’ number of cells, then all of these cells formed will have a quantization error less than the threshold quantization error.

Let’s try to comprehend the trainHVT function first before moving ahead.

trainHVT(
  dataset,
  min_compression_perc,
  n_cells,
  depth,
  quant.err,
  distance_metric = c("L1_Norm", "L2_Norm"),
  error_metric = c("mean", "max"),
  quant_method = c("kmeans", "kmedoids"),
  normalize = TRUE,
  diagnose = FALSE,
  hvt_validation = FALSE,
  train_validation_split_ratio = 0.8
)

Each of the parameters of trainHVT function have been explained below:

dataset - A dataframe, with numeric columns (features) that will be used for training the model.
min_compression_perc - An integer, indicating the minimum compression percentage to be achieved for the dataset. It indicates the desired level of reduction in dataset size compared to its original size.
n_cells - An integer, indicating the number of cells per hierarchy (level). This parameter determines the granularity or level of detail in the hierarchical vector quantization.
depth - An integer, indicating the number of levels. A depth of 1 means no hierarchy (single level), while higher values indicate multiple levels (hierarchy).
quant.error - A number indicating the quantization error threshold. A cell will only breakdown into further cells if the quantization error of the cell is above the defined quantization error threshold.
projection.scale - A number indicating the scale factor for the tesselations so as to visualize the sub-tesselations well enough. It helps in adjusting the visual representation of the hierarchy to make the sub-tesselations more visible.
scale_summary - A list with mean and standard deviation values for all the features in the dataset. Pass the scale summary when the input dataset is already scaled or normalize is set to False.
distance_metric - The distance metric can be L1_Norm(Manhattan) or L2_Norm(Eucledian). L1_Norm is selected by default. The distance metric is used to calculate the distance between an n dimensional point and centroid.
error_metric - The error metric can be mean or max. max is selected by default. max will return the max of m values and mean will take mean of m values where each value is a distance between a point and centroid of the cell.
quant_method - The quantization method can be kmeans or kmedoids. Kmeans uses means (centroids) as cluster centers while Kmedoids uses actual data points (medoids) as cluster centers. kmeans is selected by default.
normalize - A logical value indicating if the dataset should be normalized. When set to TRUE, scales the values of all features to have a mean of 0 and a standard deviation of 1 (Z-score)
diagnose - A logical value indicating whether user wants to perform diagnostics on the model. The 4th element of the hvt.result (list) contains detailed informations for debugging. Default value is TRUE.
hvt_validation - A logical value indicating whether user wants to holdout a validation set and find mean absolute deviation of the validation points from the centroid. These values can be found in the 6th element of the hvt.result (list) under the model.info under the title validation_result. Default value is FALSE.
train_validation_split_ratio - A numeric value indicating train validation split ratio. This argument is only used when hvt_validation has been set to TRUE. Default value for the argument is 0.8.

The output of trainHVT function (list of 6 elements) have been explained below:

The ‘1st element’ is a list containing information related to plotting tessellations. This information might include coordinates, boundaries, or other details necessary for visualizing the tessellations
The ‘2nd element’ is a list containing information related to Sammon’s projection coordinates of the data points in the reduced-dimensional space.
The ‘3rd element’ is a list containing detailed information about the hierarchical vector quantized data along with a summary section containing no of points, Quantization Error and the centroids for each cell.
The ‘4th element’ is a list that contains all the diagnostics information of the model when diagnose is set to TRUE.Otherwise NA
The ‘5th element’ is a list that contains all the information required to generates a Mean Absolute Deviation (MAD) plot, if hvt_validation is set to TRUE. Otherwise NA
The ‘6th element’ (model info) is a list that contains model generated timestamp, input parameters passed to the model and the validation results.

We will use the trainHVT function to compress our data while preserving essential features of the dataset. Our goal is to achieve data compression upto atleast 80%. In situations where the compression ratio does not meet the desired target, we can explore adjusting the model parameters as a potential solution. This involves making modifications to parameters such as the quantization error threshold or increasing the number of cells and then rerunning the trainHVT function again.

As this is already done in HVT Vignette: please refer for more information.

Model Parameters

Number of Cells at each Level = 900
Maximum Depth = 1
Quantization Error Threshold = 0.1
Error Metric = Max
Distance Metric = Manhattan

set.seed(240)
torus_mapA <- trainHVT(
  trainTorus_data,
  n_cells = 900,
  depth = 1,
  quant.err = 0.1,
  projection.scale = 10,
  normalize = FALSE,
  distance_metric = "L1_Norm",
  error_metric = "max",
  quant_method = "kmeans"
)

Let’s check the compression summary for torus.

compressionSummaryTable(torus_mapA[[3]]$compression_summary)

segmentLevel	noOfCells	noOfCellsBelowQuantizationError	percentOfCellsBelowQuantizationErrorThreshold	parameters
1	900	757	0.84	n_cells: 900 quant.err: 0.1 distance_metric: L1_Norm error_metric: max quant_method: kmeans

We successfully compressed 84% of the data using n_cells parameter as 900, the next step involves performing data projection on the compressed data. In this step, the compressed data will be transformed and projected onto a lower-dimensional space to visualize and analyze the data in a more manageable form.

As per the manual, torus_mapA[[3]] gives us detailed information about the hierarchical vector quantized data. torus_mapA[[3]][['summary']] gives a nice tabular data containing no of points, Quantization Error and the codebook.

The datatable displayed below is the summary from torus_mapA showing Cell.ID, Centroids and Quantization Error for each of the 900 cells.

summaryTable(torus_mapA[[3]]$summary,scroll = TRUE,limit = 500)

Segment.Level	Segment.Parent	Segment.Child	n	Cell.ID	Quant.Error	x	y	z
1	1	1	15	874	0.1	2.94	0.48	-0.19
1	1	2	11	257	0.07	-1.05	1.18	0.90
1	1	3	10	497	0.05	0.14	-1.10	-0.46
1	1	4	8	540	0.07	0.30	-1.48	-0.87
1	1	5	13	251	0.12	-0.55	2.94	0.11
1	1	6	11	324	0.08	-0.83	-1.62	0.98
1	1	7	18	814	0.1	2.25	-0.47	0.95
1	1	8	6	38	0.06	-2.79	0.40	-0.57
1	1	9	8	661	0.04	1.28	0.29	-0.72
1	1	10	10	800	0.1	2.09	1.55	0.79
1	1	11	4	389	0.03	-0.50	0.87	-0.08
1	1	12	11	886	0.09	2.81	-0.68	0.44
1	1	13	12	202	0.09	-1.35	-2.09	-0.87
1	1	14	12	817	0.1	2.46	0.60	-0.84
1	1	15	9	900	0.09	2.49	-1.66	0.05
1	1	16	14	492	0.07	0.32	1.10	0.52
1	1	17	9	650	0.06	1.20	0.94	0.88
1	1	18	11	796	0.07	1.66	-1.68	0.93
1	1	19	11	130	0.1	-2.01	-0.91	0.98
1	1	20	14	856	0.13	2.71	0.07	0.69
1	1	21	15	729	0.12	1.22	2.44	-0.67
1	1	22	18	482	0.07	0.21	1.93	1.00
1	1	23	10	89	0.07	-2.38	-1.04	-0.80
1	1	24	12	726	0.08	1.48	1.62	-0.98
1	1	25	18	858	0.11	2.66	1.30	0.24
1	1	26	8	699	0.07	1.52	0.35	-0.89
1	1	27	14	291	0.07	-0.95	-2.01	-0.97
1	1	28	18	887	0.11	2.95	-0.29	-0.23
1	1	29	10	308	0.06	-1.00	0.23	0.23
1	1	30	8	195	0.06	-1.58	-0.04	0.91
1	1	31	16	377	0.08	-0.67	-1.74	-0.99
1	1	32	12	714	0.07	1.15	-1.56	-1.00
1	1	33	8	149	0.08	-1.74	-1.88	-0.82
1	1	34	11	478	0.05	0.19	0.99	0.12
1	1	35	9	518	0.06	0.51	1.12	0.64
1	1	36	8	898	0.09	2.45	-1.67	-0.24
1	1	37	14	32	0.11	-2.07	2.14	0.17
1	1	38	10	465	0.06	-0.08	-1.09	-0.41
1	1	39	14	476	0.06	-0.08	-1.55	-0.89
1	1	40	10	449	0.06	-0.05	1.00	-0.06
1	1	41	9	288	0.05	-1.12	-0.26	-0.53
1	1	42	14	116	0.13	-1.96	-1.95	-0.64
1	1	43	11	87	0.11	-2.44	-0.12	-0.89
1	1	44	9	437	0.05	-0.30	-1.10	-0.51
1	1	45	13	666	0.12	0.30	-2.97	0.03
1	1	46	7	414	0.09	-0.10	2.96	-0.27
1	1	47	14	595	0.08	0.86	-0.56	0.21
1	1	48	2	622	0.03	0.96	1.37	-0.95
1	1	49	8	132	0.07	-2.00	-0.63	0.99
1	1	50	15	347	0.09	-0.79	-1.01	0.69
1	1	51	9	432	0.07	-0.19	1.15	-0.55
1	1	52	6	270	0.07	-0.93	-2.55	-0.70
1	1	53	21	167	0.11	-1.53	1.57	-0.97
1	1	54	13	861	0.09	2.81	1.04	0.07
1	1	55	12	305	0.07	-1.05	-0.56	-0.58
1	1	56	10	479	0.05	0.17	1.07	-0.41
1	1	57	10	304	0.06	-1.01	0.33	0.34
1	1	58	14	421	0.09	-0.17	1.42	0.81
1	1	59	12	282	0.07	-1.09	0.79	-0.76
1	1	60	8	580	0.05	0.80	1.27	-0.86
1	1	61	11	576	0.1	0.24	-2.57	0.81
1	1	62	5	582	0.05	0.77	1.46	-0.94
1	1	63	9	266	0.05	-1.22	-0.15	-0.63
1	1	64	12	636	0.09	0.73	-1.49	-0.94
1	1	65	9	503	0.07	0.16	-1.41	0.81
1	1	66	19	259	0.08	-1.19	-0.48	0.69
1	1	67	23	560	0.08	0.63	-0.82	-0.26
1	1	68	11	642	0.05	1.17	0.45	-0.66
1	1	69	13	755	0.1	0.89	-2.64	0.61
1	1	70	12	570	0.08	0.86	0.99	0.72
1	1	71	10	283	0.06	-1.07	0.50	0.57
1	1	72	14	542	0.07	0.43	-1.08	-0.54
1	1	73	8	353	0.1	-0.39	2.76	-0.60
1	1	74	9	725	0.1	1.62	1.15	-0.99
1	1	75	7	416	0.06	-0.27	1.02	0.32
1	1	76	10	346	0.07	-0.79	0.63	-0.13
1	1	77	11	375	0.05	-0.60	0.90	-0.39
1	1	78	6	269	0.06	-0.97	-1.89	0.99
1	1	79	9	532	0.04	0.58	0.82	-0.06
1	1	80	16	237	0.09	-1.13	1.49	-0.99
1	1	81	13	372	0.07	-0.46	1.43	0.87
1	1	82	9	720	0.05	1.58	1.29	1.00
1	1	83	18	471	0.1	-0.23	-2.98	-0.04
1	1	84	14	875	0.1	2.93	0.37	0.28
1	1	85	13	888	0.1	2.85	-0.68	-0.34
1	1	86	15	271	0.06	-1.15	-0.17	0.55
1	1	87	7	512	0.04	0.44	0.91	-0.17
1	1	88	7	292	0.04	-1.10	-0.12	-0.44
1	1	89	7	92	0.06	-2.34	0.76	-0.88
1	1	90	8	752	0.07	1.41	2.30	-0.71
1	1	91	11	648	0.08	1.24	0.36	0.70
1	1	92	7	548	0.06	0.70	0.73	0.15
1	1	93	13	741	0.11	1.23	2.69	0.27
1	1	94	19	811	0.1	2.03	-1.22	0.93
1	1	95	13	746	0.08	0.94	-2.45	-0.77
1	1	96	10	880	0.12	2.66	-1.09	0.48
1	1	97	7	262	0.07	-0.54	2.92	-0.23
1	1	98	10	713	0.08	1.41	-0.85	-0.93
1	1	99	11	768	0.07	1.52	-1.59	-0.98
1	1	100	11	420	0.08	-0.36	-1.35	0.80
1	1	101	16	829	0.12	2.51	1.10	0.66
1	1	102	11	847	0.1	1.74	-2.27	-0.50
1	1	103	9	2	0.08	-2.99	0.21	-0.05
1	1	104	8	43	0.07	-2.53	1.31	-0.52
1	1	105	13	222	0.09	-0.85	2.54	-0.73
1	1	106	5	264	0.04	-1.15	0.32	0.60
1	1	107	8	686	0.06	1.08	-1.38	0.97
1	1	108	9	13	0.08	-2.88	0.45	0.41
1	1	109	11	659	0.06	1.27	0.01	0.69
1	1	110	15	184	0.06	-1.53	1.13	0.99
1	1	111	9	246	0.06	-1.33	0.17	-0.75
1	1	112	6	552	0.04	0.71	0.76	0.29
1	1	113	10	210	0.1	-1.12	-2.44	0.72
1	1	114	15	547	0.09	0.53	2.14	0.97
1	1	115	13	435	0.07	-0.29	-1.91	1.00
1	1	116	8	95	0.07	-2.38	-0.84	-0.85
1	1	117	6	46	0.04	-2.76	-0.64	-0.55
1	1	118	13	86	0.08	-2.35	-0.92	0.85
1	1	119	7	724	0.07	1.59	-0.19	-0.92
1	1	120	13	643	0.06	0.99	1.60	-0.99
1	1	121	15	594	0.09	0.74	-1.04	0.69
1	1	122	13	80	0.09	-2.15	1.55	0.75
1	1	123	6	404	0.08	-0.17	2.75	-0.65
1	1	124	8	586	0.06	0.90	0.87	-0.66
1	1	125	12	19	0.1	-2.78	1.03	-0.22
1	1	126	7	111	0.08	-1.75	2.05	-0.71
1	1	127	6	24	0.07	-2.18	2.05	-0.09
1	1	128	12	680	0.09	0.77	-2.00	0.98
1	1	129	8	307	0.05	-0.96	0.63	0.53
1	1	130	12	407	0.08	-0.50	-2.07	-0.99
1	1	131	9	345	0.06	-0.79	0.73	-0.36
1	1	132	9	53	0.06	-2.63	0.13	0.77
1	1	133	10	84	0.11	-2.40	0.43	0.89
1	1	134	9	879	0.08	2.15	-1.95	0.43
1	1	135	10	620	0.06	1.07	-0.07	0.37
1	1	136	12	805	0.09	2.30	0.23	-0.95
1	1	137	12	588	0.07	0.32	-2.19	-0.97
1	1	138	13	148	0.1	-1.93	0.54	-1.00
1	1	139	20	362	0.08	-0.74	-0.71	0.23
1	1	140	7	775	0.08	1.16	-2.45	0.70
1	1	141	8	272	0.06	-1.09	1.14	-0.90
1	1	142	8	771	0.09	1.71	1.94	0.80
1	1	143	6	679	0.05	1.32	-0.21	-0.75
1	1	144	5	65	0.09	-1.80	2.34	0.30
1	1	145	17	177	0.1	-1.27	-2.67	-0.28
1	1	146	11	460	0.08	-0.14	-1.72	0.96
1	1	147	12	607	0.08	1.04	0.63	0.62
1	1	148	7	494	0.08	0.07	-1.43	-0.82
1	1	149	9	128	0.05	-2.03	-0.39	1.00
1	1	150	7	384	0.08	-0.55	-2.85	-0.42
1	1	151	8	11	0.07	-2.82	1.01	0.01
1	1	152	7	514	0.05	0.47	0.92	0.25
1	1	153	8	21	0.09	-2.91	0.00	-0.40
1	1	154	7	683	0.05	1.32	1.34	0.99
1	1	155	8	427	0.07	-0.20	1.50	-0.87
1	1	156	9	491	0.06	0.31	1.27	0.72
1	1	157	11	90	0.07	-2.14	1.42	-0.82
1	1	158	13	721	0.08	1.65	0.11	0.94
1	1	159	9	186	0.07	-1.61	-0.50	0.95
1	1	160	18	784	0.1	1.73	-1.32	-0.98
1	1	161	10	728	0.05	1.68	0.49	-0.97
1	1	162	10	181	0.06	-1.70	0.71	-0.98
1	1	163	8	789	0.08	1.27	-2.34	-0.74
1	1	164	7	293	0.06	-1.00	0.76	0.66
1	1	165	6	16	0.08	-2.87	-0.23	0.46
1	1	166	7	144	0.09	-1.78	-1.62	0.91
1	1	167	12	115	0.07	-1.86	1.61	0.88
1	1	168	8	403	0.04	-0.39	0.92	0.05
1	1	169	8	651	0.08	0.82	2.45	0.80
1	1	170	7	190	0.09	-0.96	2.70	-0.49
1	1	171	5	168	0.07	-1.66	-1.61	-0.95
1	1	172	8	164	0.06	-1.75	0.50	0.98
1	1	173	11	690	0.09	0.73	-2.26	0.92
1	1	174	9	367	0.07	-0.64	-2.69	-0.64
1	1	175	12	156	0.05	-1.81	-0.52	0.99
1	1	176	12	94	0.08	-2.07	-1.76	0.69
1	1	177	7	877	0.09	2.66	-1.08	-0.48
1	1	178	9	114	0.08	-1.74	-2.42	0.20
1	1	179	11	751	0.06	1.64	-0.85	-0.99
1	1	180	8	314	0.07	-0.95	0.95	-0.75
1	1	181	14	433	0.08	-0.14	1.16	0.55
1	1	182	14	574	0.08	0.89	0.54	-0.28
1	1	183	23	142	0.1	-2.04	-0.33	-0.99
1	1	184	10	328	0.07	-0.89	0.45	-0.07
1	1	185	12	841	0.08	2.70	0.62	-0.64
1	1	186	8	411	0.06	-0.12	2.87	-0.48
1	1	187	12	240	0.06	-1.30	-0.02	0.71
1	1	188	11	385	0.06	-0.60	-1.41	-0.88
1	1	189	10	249	0.05	-1.25	0.17	0.68
1	1	190	3	274	0.04	-1.18	0.04	-0.57
1	1	191	17	31	0.07	-2.84	-0.56	-0.45
1	1	192	13	131	0.12	-1.59	-2.51	-0.20
1	1	193	13	579	0.08	0.73	1.67	-0.98
1	1	194	10	499	0.06	0.27	2.90	0.40
1	1	195	10	718	0.05	1.53	-0.48	-0.92
1	1	196	16	535	0.08	0.32	-1.25	-0.70
1	1	197	8	857	0.09	2.51	1.62	0.13
1	1	198	13	213	0.06	-1.53	-0.14	-0.88
1	1	199	7	40	0.1	-2.41	1.43	0.58
1	1	200	5	33	0.05	-2.79	-0.87	-0.38
1	1	201	17	525	0.08	0.39	-0.92	0.03
1	1	202	11	834	0.07	2.03	-1.58	-0.82
1	1	203	17	825	0.11	2.48	0.24	0.86
1	1	204	9	505	0.07	0.29	2.91	-0.37
1	1	205	9	93	0.08	-2.30	-0.59	0.92
1	1	206	11	804	0.08	2.33	0.91	0.86
1	1	207	13	57	0.09	-2.29	-1.79	0.41
1	1	208	5	85	0.07	-2.46	0.39	-0.87
1	1	209	11	626	0.06	1.08	0.92	-0.81
1	1	210	7	500	0.11	-0.10	-2.94	0.31
1	1	211	11	895	0.08	2.75	-1.13	-0.20
1	1	212	16	785	0.09	2.05	1.27	-0.91
1	1	213	6	225	0.05	-1.25	1.22	0.97
1	1	214	14	296	0.07	-0.89	1.42	-0.94
1	1	215	7	344	0.05	-0.73	0.87	0.50
1	1	216	7	280	0.04	-1.01	-1.42	0.96
1	1	217	16	624	0.09	1.10	0.11	0.45
1	1	218	8	745	0.06	1.58	1.78	0.92
1	1	219	9	806	0.08	2.18	1.53	-0.74
1	1	220	10	52	0.12	-2.29	-1.93	0.03
1	1	221	14	456	0.05	-0.12	-1.04	0.29
1	1	222	11	315	0.05	-0.98	0.26	-0.18
1	1	223	11	480	0.05	-0.02	-1.32	-0.73
1	1	224	7	1	0.09	-2.96	0.35	0.16
1	1	225	9	209	0.06	-1.39	-1.68	-0.98
1	1	226	15	700	0.1	1.01	2.64	0.55
1	1	227	14	779	0.11	1.87	-0.82	1.00
1	1	228	7	191	0.06	-1.64	-1.13	-1.00
1	1	229	9	634	0.08	0.63	-1.70	-0.98
1	1	230	9	136	0.1	-1.59	-2.31	0.58
1	1	231	9	669	0.06	1.21	1.40	-0.99
1	1	232	6	794	0.06	1.76	2.13	0.64
1	1	233	15	782	0.1	1.58	2.41	-0.46
1	1	234	8	778	0.06	1.97	-0.36	1.00
1	1	235	12	827	0.11	2.26	-0.95	0.88
1	1	236	14	554	0.06	0.56	-0.83	0.05
1	1	237	8	706	0.06	1.55	0.75	-0.96
1	1	238	9	107	0.1	-2.31	0.16	-0.94
1	1	239	14	539	0.08	0.36	-1.45	0.86
1	1	240	6	15	0.06	-2.92	0.23	-0.37
1	1	241	7	374	0.05	-0.66	-0.91	0.49
1	1	242	9	263	0.08	-1.23	0.26	-0.67
1	1	243	7	206	0.05	-1.51	0.79	-0.95
1	1	244	10	415	0.04	-0.29	0.97	0.14
1	1	245	19	609	0.11	0.42	-2.16	0.97
1	1	246	7	864	0.07	1.82	-2.32	-0.30
1	1	247	8	275	0.08	-1.18	-0.68	-0.77
1	1	248	13	390	0.09	-0.52	-1.76	0.98
1	1	249	11	373	0.08	-0.35	2.38	-0.91
1	1	250	11	26	0.08	-2.42	1.63	-0.39
1	1	251	5	550	0.04	0.70	0.72	-0.04
1	1	252	8	543	0.05	0.54	1.86	1.00
1	1	253	10	673	0.1	0.48	-2.58	-0.77
1	1	254	13	583	0.06	0.74	-0.84	-0.47
1	1	255	14	601	0.09	0.92	-0.39	-0.02
1	1	256	7	30	0.07	-2.69	-1.15	0.37
1	1	257	10	707	0.08	0.98	-1.84	-0.99
1	1	258	12	753	0.1	1.85	0.42	0.99
1	1	259	8	742	0.08	1.22	2.74	-0.02
1	1	260	11	287	0.1	-0.57	2.63	-0.71
1	1	261	13	200	0.08	-1.48	-1.09	0.98
1	1	262	10	820	0.12	1.52	-2.34	0.61
1	1	263	14	281	0.12	-0.55	2.47	0.84
1	1	264	8	102	0.09	-1.97	1.64	-0.82
1	1	265	7	667	0.05	0.62	-2.13	-0.97
1	1	266	7	681	0.06	1.39	0.88	-0.93
1	1	267	10	365	0.08	-0.43	2.13	-0.98
1	1	268	13	447	0.11	-0.31	-2.62	-0.76
1	1	269	11	48	0.09	-2.68	0.42	0.70
1	1	270	10	124	0.08	-2.14	-1.31	-0.85
1	1	271	13	533	0.06	0.59	0.95	0.46
1	1	272	13	687	0.13	0.96	2.68	-0.52
1	1	273	16	79	0.13	-2.24	-1.79	-0.48
1	1	274	13	42	0.1	-2.53	1.18	0.59
1	1	275	12	327	0.07	-0.90	0.57	-0.35
1	1	276	10	892	0.09	2.81	-0.94	0.26
1	1	277	16	252	0.08	-1.18	-1.03	0.90
1	1	278	14	417	0.1	-0.40	-2.47	0.86
1	1	279	6	289	0.05	-1.10	0.05	-0.44
1	1	280	8	777	0.07	2.02	1.26	0.92
1	1	281	7	885	0.11	2.99	0.05	-0.08
1	1	282	8	230	0.05	-1.41	-0.86	-0.94
1	1	283	10	36	0.09	-2.21	1.91	-0.37
1	1	284	15	311	0.05	-1.00	-0.05	0.06
1	1	285	9	81	0.08	-2.34	1.23	-0.76
1	1	286	15	838	0.11	2.61	0.22	-0.78
1	1	287	7	189	0.04	-1.57	0.65	0.96
1	1	288	13	844	0.12	2.45	-0.68	0.83
1	1	289	10	495	0.07	0.31	1.51	0.89
1	1	290	13	549	0.06	0.69	0.75	-0.19
1	1	291	9	73	0.08	-2.03	1.95	-0.58
1	1	292	10	198	0.06	-1.63	-0.36	-0.94
1	1	293	13	691	0.06	1.46	0.00	0.84
1	1	294	8	754	0.08	1.23	-1.92	0.96
1	1	295	9	534	0.04	0.59	0.84	0.20
1	1	296	12	323	0.08	-0.85	0.95	0.69
1	1	297	16	522	0.12	0.39	2.68	0.70
1	1	298	5	662	0.03	1.28	0.52	-0.78
1	1	299	18	553	0.08	0.47	-1.20	0.71
1	1	300	18	867	0.13	2.22	-1.65	0.64
1	1	301	8	430	0.1	-0.39	-2.33	-0.93
1	1	302	7	490	0.05	0.30	0.95	-0.03
1	1	303	5	678	0.06	1.35	0.11	-0.77
1	1	304	10	120	0.12	-1.80	1.82	-0.83
1	1	305	13	584	0.07	0.77	-0.84	0.50
1	1	306	12	719	0.13	0.58	-2.86	-0.37
1	1	307	7	51	0.08	-2.75	-0.11	-0.65
1	1	308	17	356	0.07	-0.79	-0.63	-0.11
1	1	309	9	558	0.1	0.48	2.95	-0.04
1	1	310	9	555	0.06	0.30	-1.71	-0.96
1	1	311	13	173	0.07	-1.77	0.18	-0.97
1	1	312	9	54	0.12	-1.89	2.31	-0.12
1	1	313	14	709	0.08	1.42	-0.76	0.92
1	1	314	11	708	0.08	1.55	0.09	-0.89
1	1	315	7	227	0.07	-1.39	0.22	0.80
1	1	316	9	883	0.1	2.10	-2.11	0.22
1	1	317	8	401	0.1	-0.16	2.99	0.09
1	1	318	13	96	0.08	-1.56	2.43	0.45
1	1	319	6	364	0.04	-0.68	0.74	-0.02
1	1	320	8	521	0.06	0.13	-1.79	-0.98
1	1	321	2	546	0.01	0.64	1.04	-0.63
1	1	322	16	459	0.08	-0.12	-1.47	0.85
1	1	323	10	510	0.07	-0.01	-2.28	-0.96
1	1	324	10	387	0.08	-0.32	1.71	0.96
1	1	325	4	383	0.03	-0.54	0.84	-0.04
1	1	326	14	363	0.11	-0.36	2.23	0.96
1	1	327	17	297	0.08	-1.04	-0.37	0.43
1	1	328	7	869	0.11	2.75	-0.49	-0.60
1	1	329	10	98	0.1	-2.25	-1.09	0.86
1	1	330	14	544	0.07	0.49	-0.94	-0.35
1	1	331	14	242	0.07	-1.29	0.91	-0.90
1	1	332	14	590	0.06	0.96	0.51	0.41
1	1	333	13	354	0.12	-0.34	2.61	0.77
1	1	334	9	12	0.07	-2.89	0.76	-0.09
1	1	335	9	840	0.09	2.52	-0.30	-0.84
1	1	336	10	545	0.06	0.58	1.31	-0.82
1	1	337	9	872	0.12	2.74	-0.41	0.63
1	1	338	10	496	0.06	0.34	0.95	0.12
1	1	339	7	162	0.08	-1.33	-2.67	0.12
1	1	340	7	783	0.09	2.11	0.68	-0.97
1	1	341	6	228	0.05	-1.45	0.27	-0.85
1	1	342	11	409	0.06	-0.47	-1.18	-0.68
1	1	343	6	267	0.07	-1.22	-0.32	-0.67
1	1	344	6	767	0.06	1.97	0.41	-1.00
1	1	345	15	133	0.11	-1.49	2.24	-0.72
1	1	346	8	39	0.07	-2.78	-0.33	-0.59
1	1	347	10	443	0.05	-0.09	1.01	0.14
1	1	348	9	250	0.09	-0.63	2.81	-0.47
1	1	349	6	68	0.09	-1.89	2.13	0.51
1	1	350	7	839	0.11	1.51	-2.55	-0.24
1	1	351	11	388	0.06	-0.44	1.36	-0.82
1	1	352	10	694	0.08	1.24	1.86	0.97
1	1	353	11	76	0.09	-2.06	-2.14	0.25
1	1	354	10	795	0.1	1.15	-2.64	0.48
1	1	355	16	434	0.1	-0.01	2.56	0.82
1	1	356	13	10	0.07	-2.69	1.30	0.14
1	1	357	10	464	0.05	0.10	1.10	0.44
1	1	358	12	247	0.06	-1.33	0.00	-0.74
1	1	359	6	889	0.08	2.63	-1.31	-0.34
1	1	360	7	612	0.06	1.00	-0.21	-0.18
1	1	361	7	125	0.06	-2.07	0.37	0.99
1	1	362	8	878	0.09	1.96	-2.27	0.05
1	1	363	16	338	0.11	-0.50	1.96	1.00
1	1	364	12	652	0.06	1.01	-0.86	-0.74
1	1	365	15	793	0.09	2.16	0.54	0.97
1	1	366	5	61	0.06	-2.64	0.29	-0.76
1	1	367	15	891	0.12	2.94	-0.48	0.19
1	1	368	6	592	0.05	0.39	-1.96	-1.00
1	1	369	11	408	0.08	-0.43	-2.12	0.98
1	1	370	11	318	0.08	-0.97	-1.22	-0.90
1	1	371	14	74	0.07	-2.51	-0.28	0.85
1	1	372	9	734	0.07	0.90	-2.43	0.80
1	1	373	9	310	0.06	-1.00	0.12	0.11
1	1	374	13	35	0.11	-2.50	-1.63	-0.13
1	1	375	14	615	0.07	1.03	0.06	-0.27
1	1	376	18	527	0.07	0.20	-1.81	0.98
1	1	377	12	410	0.06	-0.45	-0.96	-0.35
1	1	378	9	398	0.06	-0.43	0.94	0.24
1	1	379	7	781	0.06	1.75	-1.23	0.99
1	1	380	9	688	0.07	0.67	-2.34	-0.90
1	1	381	13	135	0.12	-1.37	2.33	0.71
1	1	382	9	321	0.06	-0.96	0.41	-0.30
1	1	383	11	424	0.08	-0.39	-1.42	-0.85
1	1	384	8	397	0.06	-0.53	-0.86	0.14
1	1	385	11	169	0.09	-0.98	2.81	-0.21
1	1	386	11	868	0.08	2.82	-0.11	-0.56
1	1	387	9	854	0.09	2.40	-1.25	-0.71
1	1	388	9	809	0.09	1.31	-2.57	-0.45
1	1	389	6	7	0.05	-2.34	1.87	0.03
1	1	390	8	165	0.05	-1.76	-1.36	-0.97
1	1	391	6	682	0.07	1.41	0.63	-0.89
1	1	392	10	761	0.06	1.80	-0.39	-0.98
1	1	393	10	193	0.09	-1.19	-2.65	0.41
1	1	394	14	799	0.13	1.90	1.94	-0.69
1	1	395	10	704	0.06	1.38	1.56	1.00
1	1	396	5	295	0.07	-0.91	-2.30	-0.88
1	1	397	15	395	0.09	-0.38	1.22	0.69
1	1	398	11	216	0.07	-1.44	-0.18	0.83
1	1	399	12	221	0.05	-1.19	1.43	0.99
1	1	400	12	523	0.1	0.38	2.72	-0.66
1	1	401	11	215	0.06	-1.49	0.51	-0.90
1	1	402	5	569	0.07	0.57	2.82	-0.47
1	1	403	9	104	0.06	-2.30	0.55	-0.93
1	1	404	8	824	0.1	2.01	-1.52	0.85
1	1	405	11	214	0.09	-0.85	2.40	0.83
1	1	406	18	219	0.11	-0.95	2.32	-0.86
1	1	407	7	4	0.08	-2.96	-0.25	0.20
1	1	408	8	760	0.07	1.74	-0.65	-0.99
1	1	409	12	641	0.06	1.16	0.07	-0.54
1	1	410	7	261	0.06	-1.22	0.47	-0.72
1	1	411	7	371	0.06	-0.63	0.79	-0.15
1	1	412	15	613	0.07	0.98	-0.40	0.33
1	1	413	15	187	0.08	-1.69	-0.90	-0.99
1	1	414	15	677	0.08	1.33	-0.29	0.77
1	1	415	11	166	0.09	-1.71	-0.89	0.99
1	1	416	6	379	0.06	-0.59	0.81	0.10
1	1	417	16	212	0.06	-1.53	0.07	-0.88
1	1	418	15	224	0.11	-0.98	-2.82	0.11
1	1	419	12	359	0.07	-0.79	-0.81	-0.50
1	1	420	11	376	0.07	-0.68	-0.79	-0.30
1	1	421	9	143	0.09	-1.88	-1.24	0.96
1	1	422	15	656	0.08	0.77	-1.70	0.99
1	1	423	6	302	0.04	-1.03	0.44	-0.48
1	1	424	9	163	0.06	-1.82	-1.18	-0.98
1	1	425	11	431	0.07	-0.08	1.77	0.97
1	1	426	14	234	0.06	-1.34	-0.30	0.78
1	1	427	14	602	0.12	0.20	-2.81	-0.56
1	1	428	14	664	0.1	1.33	0.63	0.85
1	1	429	14	147	0.1	-1.62	-2.05	0.78
1	1	430	13	849	0.12	2.50	1.55	-0.32
1	1	431	10	561	0.05	0.81	0.59	0.04
1	1	432	8	183	0.07	-1.65	0.23	0.94
1	1	433	13	100	0.06	-2.24	0.57	0.95
1	1	434	14	573	0.07	0.75	-0.66	-0.04
1	1	435	11	749	0.09	1.80	0.05	-0.98
1	1	436	13	350	0.08	-0.82	-0.58	0.10
1	1	437	10	655	0.08	1.17	-0.31	-0.61
1	1	438	9	440	0.1	0.01	2.78	0.61
1	1	439	7	3	0.08	-2.99	-0.07	-0.14
1	1	440	13	231	0.07	-1.38	-1.09	-0.97
1	1	441	9	313	0.07	-1.01	-0.78	-0.69
1	1	442	12	848	0.11	2.30	1.91	0.05
1	1	443	15	220	0.06	-1.48	-0.57	-0.91
1	1	444	9	366	0.09	-0.62	-2.93	-0.01
1	1	445	8	22	0.09	-2.28	1.85	0.34
1	1	446	15	764	0.12	1.76	1.63	-0.91
1	1	447	14	6	0.1	-2.54	1.54	0.22
1	1	448	11	765	0.1	0.81	-2.88	0.05
1	1	449	19	604	0.06	0.99	0.36	-0.32
1	1	450	10	774	0.09	2.03	0.14	-1.00
1	1	451	8	788	0.08	1.53	2.57	-0.08
1	1	452	9	710	0.07	1.54	-0.25	0.90
1	1	453	11	157	0.09	-1.41	-2.49	0.49
1	1	454	8	816	0.08	1.79	-1.80	-0.84
1	1	455	13	850	0.08	1.88	-2.08	0.59
1	1	456	9	126	0.08	-1.34	2.65	-0.21
1	1	457	11	182	0.06	-1.72	0.44	-0.97
1	1	458	7	97	0.07	-2.29	0.00	0.95
1	1	459	6	188	0.05	-1.41	1.36	1.00
1	1	460	11	716	0.14	1.19	2.34	0.77
1	1	461	13	334	0.07	-0.87	-0.68	0.44
1	1	462	14	412	0.07	-0.40	-0.98	0.35
1	1	463	18	787	0.11	1.02	-2.77	-0.29
1	1	464	14	461	0.07	0.10	1.33	0.74
1	1	465	17	392	0.08	-0.44	1.03	0.48
1	1	466	12	803	0.08	2.02	1.84	0.68
1	1	467	10	631	0.07	1.13	0.79	0.78
1	1	468	14	498	0.06	0.18	-0.99	-0.08
1	1	469	11	692	0.06	1.35	-0.59	-0.85
1	1	470	11	320	0.07	-0.95	0.68	-0.55
1	1	471	15	587	0.08	0.64	-1.21	-0.77
1	1	472	13	357	0.08	-0.60	1.49	-0.92
1	1	473	16	833	0.1	1.86	-1.85	0.78
1	1	474	5	472	0.05	0.17	1.46	0.85
1	1	475	12	600	0.07	0.86	-0.69	0.44
1	1	476	7	91	0.1	-1.97	-2.05	0.53
1	1	477	13	303	0.06	-0.78	1.67	-0.98
1	1	478	11	823	0.1	1.36	-2.66	-0.04
1	1	479	9	515	0.06	0.30	-1.01	-0.31
1	1	480	12	8	0.09	-2.46	1.70	-0.10
1	1	481	11	563	0.07	0.84	0.86	0.60
1	1	482	14	294	0.05	-1.06	0.12	0.35
1	1	483	7	455	0.07	-0.19	-1.39	-0.80
1	1	484	10	393	0.04	-0.57	-0.82	0.00
1	1	485	9	832	0.07	2.37	-0.70	-0.88
1	1	486	14	504	0.08	0.20	-1.21	0.63
1	1	487	13	632	0.07	0.93	-0.95	0.74
1	1	488	16	853	0.14	2.78	0.93	-0.33
1	1	489	12	723	0.1	1.34	2.00	-0.91
1	1	490	12	526	0.09	0.39	2.41	-0.89
1	1	491	10	88	0.07	-2.28	-1.51	-0.67
1	1	492	13	58	0.11	-2.07	1.89	0.59
1	1	493	12	245	0.11	-0.92	-2.79	-0.32
1	1	494	7	64	0.05	-2.18	-2.06	0.10
1	1	495	10	702	0.08	1.44	1.29	-0.99
1	1	496	9	473	0.07	0.11	1.18	-0.58
1	1	497	8	205	0.08	-1.23	-2.02	0.93
1	1	498	11	568	0.06	0.63	-1.00	-0.58
1	1	499	10	329	0.06	-0.77	-2.51	-0.78
1	1	500	13	105	0.1	-1.56	2.45	-0.40

Now let us understand what each column in the above table means:

Segment.Level - Level of the cell. In this case, we have performed Vector Quantization for depth 1. Hence Segment Level is 1.
Segment.Parent - Parent segment of the cell.
Segment.Child (Cell.Number) - The children of a particular cell. In this case, it is the total number of cells at which we achieved the defined compression percentage.
n - No of points in each cell.
Cell.ID - Cell_ID’s are generated for the multivariate data using 1-D Sammon’s Projection algorithm.
Quant.Error - Quantization Error for each cell.

All the columns after this will contain centroids for each cell. They can also be called a codebook, which represents a collection of all centroids or codewords.

Now let’s try to understand plotHVT function. The parameters have been explained in detail below:

plotHVT <-(hvt.results, line.width, color.vec, pch1 = 21, palette.color = 6, centroid.size = 1.5, title = NULL, maxDepth = NULL, dataset, child.level, hmap.cols, previous_level_heatmap = TRUE, show.points = FALSE, asp = 1, ask = TRUE, tess.label = NULL, quant.error.hmap = NULL, n_cells.hmap = NULL, label.size = 0.5, sepration_width = 7, layer_opacity = c(0.5, 0.75, 0.99), dim_size = 1000, heatmap = '2Dhvt')

hvt.results - (1D/2Dhvt/2Dheatmap/surface_plot) A list (hvt.result) obtained from the trainHVT function while performing hierarchical vector quantization on training data. This list provides an overview of the hierarchical vector quantized data, including diagnostics, tessellation details, Sammon’s projection coordinates, and model input information.
line.width - (2Dhvt/2Dheatmap) A vector indicating the line widths of the tessellation boundaries for each layer.
color.vec - (2Dhvt/2Dheatmap) A vector indicating the colors of the tessellations boundaries at each layer.
pch1 - (2Dhvt/2Dheatmap) Symbol, It plots the centroids with a particular symbol such as (solid circle, bullet, filled square, filled diamond) in the tessellations.(default = 21 i.e filled circle).
centroid.size - (2Dhvt/2Dheatmap) Size of centroids for each level of tessellations (default = 3).
title - (2Dhvt) Set a title for the plot (default = NULL).
maxDepth - (2Dhvt) An integer indicating the number of levels. (default = NULL)
palette.color - (2Dheatmap) A number indicating the heat map color palette. 1 - rainbow,2 - heat.colors, 3 - terrain.colors, 4 - topo.colors, 5 - cm.colors, 6 - BlCyGrYlRd (Blue,Cyan,Green,Yellow,Red) color (default= 6).
dataset - (2Dheatmap) Data frame. The input dataset.
child.level - (2Dheatmap/surface_plot) A Number indicating the level for which the heat map is to be plotted.
hmap.cols - (2Dheatmap/surface_plot) A Number or a Character which is the column number of column name from the dataset indicating the variables for which the heat map is to be plotted.
previous_level_heatmap - (2Dheatmap) A Logical value to indicate whether the heatmap of previous level will be overlayed on the heatmap of selected level.
show.points - (2Dheatmap) A Logical value indicating if the centroids should be plotted on the tessellations. (default = FALSE)
asp - (2Dheatmap) A Number indicating the aspect ratio type. For flexible aspect ratio set, asp = NA. (default = 1)
ask - (2Dheatmap) A Logical value to have interactive R session.(default = TRUE)
tess.label - (2Dheatmap) A vector for labelling the tessellations. (default = NULL)
label.size - (2Dheatmap) The size by which the tessellation labels should be scaled.(default = 0.5)
quant.error.hmap - (2Dheatmap) A number indicating the quantization error threshold.
n_cells.hmap - (2Dheatmap) An integer indicating the number of cells/clusters per hierarchy
sepration_width - (surface_plot) An integer indicating the width between two Levels.
layer_opacity - (surface_plot) A vector indicating the opacity of each layer/ level.
dim_size - (surface_plot) An integer indicating the dimension size used to create the matrix for the plot.
heatmap - A Character indicating which type of plot should be generated. Accepted entries are ‘1D’,‘2Dhvt’,‘2Dheatmap’, ‘surface_plot’. Default value is 2Dhvt.

Let’s plot the Voronoi tessellation for layer 1 (map A).

plotHVT(torus_mapA,
        line.width = c(0.4), 
        color.vec = c("#141B41"),
        centroid.size = 0.01,
        maxDepth = 1, heatmap = '2Dhvt')

Figure 2: The Voronoi Tessellation for layer 1 (map A) shown for the 900 cells in the dataset ’torus’

Heat Maps

We will now overlay all the features as heatmap over the Voronoi Tessellation plot for better visualization and identification of patterns, trends, and variations in the data.

Now let’s plot the Voronoi Tessellation with the heatmap overlaid for all the features in the torus data for better visualization and interpretation of data patterns and distributions.

The heatmaps displayed below provides a visual representation of the spatial characteristics of the torus data, allowing us to observe patterns and trends in the distribution of each of the features (x,y,z). The sheer green shades highlight regions with higher values in each of the heatmaps, while the indigo shades indicate areas with the lowest values in each of the heatmaps. By analyzing these heatmaps, we can gain insights into the variations and relationships between each of these features within the torus data.


  plotHVT(
  torus_mapA,
  trainTorus_data,
  child.level = 1,
  hmap.cols = "x",
  line.width = c(0.2),
  color.vec = c("#141B41"),
  palette.color = 6,
  centroid.size = 0.1,
  show.points = TRUE,
  quant.error.hmap = 0.2,
  n_cells.hmap = 900,
  heatmap = '2Dheatmap'
)

Figure 4: The Voronoi Tessellation with the heat map overlaid for variable ’x’ in the ’torus’ dataset


  plotHVT(
  torus_mapA,
  trainTorus_data,
  child.level = 1,
  hmap.cols = "y",
  line.width = c(0.2),
  color.vec = c("#141B41"),
  palette.color = 6,
  centroid.size = 0.1,
  show.points = TRUE,
  quant.error.hmap = 0.2,
  n_cells.hmap = 900,
  heatmap = '2Dheatmap'
)

Figure 5: The Voronoi Tessellation with the heat map overlaid for variable ’y’ in the ’torus’ dataset


  plotHVT(
  torus_mapA,
  trainTorus_data,
  child.level = 1,
  hmap.cols = "z",
  line.width = c(0.2),
  color.vec = c("#141B41"),
  palette.color = 6,
  centroid.size = 0.1,
  show.points = TRUE,
  quant.error.hmap = 0.2,
  n_cells.hmap = 440,
  heatmap = '2Dheatmap'
)

Figure 6: The Voronoi Tessellation with the heat map overlaid for variable ’z’ in the ’torus’ dataset

4. Map B : Compressed Novelty Map

Let us try to visualize the Map B from the flow diagram below.

Figure 10: Data Segregation with highlighted bounding box in red around map B

In this section, we will manually figure out the novelty cells from the plotted torus_mapA and store it in identified_Novelty_cells variable.

Note: For manual selecting the novelty cells from map A, one can enhance its interactivity by adding plotly elements to the code. This will transform map A into an interactive plot, allowing users to actively engage with the data. By hovering over the centroids of the cells, a tag containing segment child information will be displayed. Users can explore the map by hovering over different cells and selectively choose the novelty cells they wish to consider. Added an image for reference.

Figure 11: Manually selecting novelty cells

The removeNovelty function removes the identified novelty cell(s) from the training dataset (containing 9600 datapoints) and stores those records separately.

It takes input as the cell number (Segment.Child) of the manually identified novelty cell(s) and the compressed HVT map (torus_mapA) with 900 cells. It returns a list of two items: data with novelty, and a subset of the data without novelty.

NOTE: As we are using torus data here, the identified novelty cells given are for demo purpose.

identified_Novelty_cells <<- c(478,448,626,220,374,644,442,197)   #as a example
output_list <- removeNovelty(identified_Novelty_cells, torus_mapA)
data_with_novelty <- output_list[[1]]
data_without_novelty <- output_list[[2]]

Let’s have a look at the data with novelty(containing 78 records). For the sake of brevity, we will only show the first 20 rows.

novelty_data <- data_with_novelty
novelty_data$Row.No <- row.names(novelty_data)
novelty_data <- novelty_data %>% dplyr::select("Row.No","Cell.ID","Cell.Number","x","y","z")
colnames(novelty_data) <- c("Row.No","Cell.ID","Segment.Child","x","y","z")
novelty_data %>% head(100) %>% 
  as.data.frame() %>%
  Table(scroll = TRUE, limit = 20)

Row.No	Cell.ID	Segment.Child	x	y	z
1	857	197	2.4975	1.6226	0.2071
2	857	197	2.4936	1.6507	0.1380
3	857	197	2.5783	1.5276	0.0794
4	857	197	2.4381	1.7455	0.0552
5	857	197	2.4653	1.7095	0.0057
6	857	197	2.4886	1.5752	0.3264
7	857	197	2.5611	1.5621	-0.0136
8	857	197	2.5374	1.5475	0.2346
9	52	220	-2.2472	-1.9850	0.0571
10	52	220	-2.2326	-2.0003	-0.0687
11	52	220	-2.2476	-1.9798	-0.0977
12	52	220	-2.2374	-1.9752	-0.1755
13	52	220	-2.3188	-1.8912	0.1244
14	52	220	-2.3080	-1.9028	0.1321
15	52	220	-2.2446	-1.9892	0.0410
16	52	220	-2.4092	-1.7780	0.1069
17	52	220	-2.2843	-1.9121	0.2041
18	52	220	-2.3390	-1.8785	0.0041
19	35	374	-2.4310	-1.7577	-0.0142
20	35	374	-2.4425	-1.7417	-0.0149

4.1 Voronoi Tessellation with highlighted novelty cell

The plotNovelCells function is used to plot the Voronoi tessellation using the compressed HVT map (torus_mapA) containing 900 cells and highlights the identified novelty cell(s) i.e 8 cells (containing 78 records) in red on the map.

plotNovelCells(identified_Novelty_cells, torus_mapA,line.width = c(0.4),centroid.size = 0.01)

Figure 12: The Voronoi Tessellation constructed using the compressed HVT map (map A) with the novelty cell(s) highlighted in red

We pass the dataframe with novelty records (78 records) to trainHVT function along with other model parameters mentioned below to generate map B (layer2)

Model Parameters

Number of Cells at each Level = 11
Maximum Depth = 1
Quantization Error Threshold = 0.1
Error Metric = Max
Distance Metric = Manhattan

colnames(data_with_novelty) <- c("Cell.ID","Segment.Child","x","y","z")
data_with_novelty <- data_with_novelty[,-1:-2]
torus_mapB <- list()
mapA_scale_summary = torus_mapA[[3]]$scale_summary
torus_mapB <- trainHVT(data_with_novelty,
                  n_cells = 11,   
                  depth = 1,
                  quant.err = 0.1,
                  projection.scale = 10,
                  normalize = FALSE,
                  distance_metric = "L1_Norm",
                  error_metric = "max",
                  quant_method = "kmeans"
                  )

The datatable displayed below is the summary from map B (layer 2) showing Cell.ID, Centroids and Quantization Error for each of the 11 cells.

summaryTable(torus_mapB[[3]]$summary,scroll = TRUE,limit = 500)

Segment.Level	Segment.Parent	Segment.Child	n	Cell.ID	Quant.Error	x	y	z
1	1	1	5	6	0.05	-2.01	-2.22	-0.05
1	1	2	5	3	0.08	1.75	-2.43	-0.08
1	1	3	6	10	0.06	-2.44	-1.73	-0.10
1	1	4	7	11	0.08	-2.55	-1.54	-0.16
1	1	5	9	1	0.09	2.28	1.94	0.02
1	1	6	11	4	0.1	1.36	-2.66	-0.04
1	1	7	3	9	0.04	-2.10	-2.13	-0.12
1	1	8	5	7	0.06	-2.33	-1.87	0.11
1	1	9	5	8	0.05	-2.24	-1.99	-0.05
1	1	10	11	5	0.1	0.81	-2.88	0.05
1	1	11	11	2	0.13	2.47	1.67	0.13

Now let’s check the compression summary for HVT (torus_mapB). The table below shows no of cells, no of cells having quantization error below threshold and percentage of cells having quantization error below threshold for each level.

mapB_compression_summary <- torus_mapB[[3]]$compression_summary %>%  dplyr::mutate_if(is.numeric, funs(round(.,4)))
compressionSummaryTable(mapB_compression_summary)

segmentLevel	noOfCells	noOfCellsBelowQuantizationError	percentOfCellsBelowQuantizationErrorThreshold	parameters
1	11	9	0.82	n_cells: 11 quant.err: 0.1 distance_metric: L1_Norm error_metric: max quant_method: kmeans

As it can be seen from the table above, 82% of the cells have hit the quantization threshold error.Since we are successfully able to attain the desired compression percentage, so we will not further subdivide the cells

5. Map C : Compressed Map without Novelty

Let us try to visualize the compressed Map C from the flow diagram below.

Figure 13:Data Segregation with highlighted bounding box in red around compressed map C

5.1 Iteration 1:

With the Novelties removed, we construct another hierarchical Voronoi tessellation map C layer 2 on the data without Novelty (containing 9522 records) and below mentioned model parameters.

Model Parameters

Number of Cells at each Level = 10
Maximum Depth = 2
Quantization Error Threshold = 0.1
Error Metric = Max
Distance Metric = Manhattan

torus_mapC <- list()
mapA_scale_summary = torus_mapA[[3]]$scale_summary
torus_mapC <- trainHVT(data_without_novelty,
                  n_cells = 10,
                  depth = 2,
                  quant.err = 0.1,
                  projection.scale = 10,
                  normalize = FALSE,
                  distance_metric = "L1_Norm",
                  error_metric = "max",
                  quant_method = "kmeans",
                  diagnose = FALSE,
                  scale_summary = mapA_scale_summary)

Now let’s check the compression summary for HVT (torus_mapC) where n_cell was set to 10. The table below shows no of cells, no of cells having quantization error below threshold and percentage of cells having quantization error below threshold for each level.

mapC_compression_summary <- torus_mapC[[3]]$compression_summary %>%  dplyr::mutate_if(is.numeric, funs(round(.,4)))
compressionSummaryTable(mapC_compression_summary)

segmentLevel	noOfCells	noOfCellsBelowQuantizationError	percentOfCellsBelowQuantizationErrorThreshold	parameters
1	10	0	0	n_cells: 10 quant.err: 0.1 distance_metric: L1_Norm error_metric: max quant_method: kmeans
2	100	0	0	n_cells: 10 quant.err: 0.1 distance_metric: L1_Norm error_metric: max quant_method: kmeans

As it can be seen from the table above, 0% of the cells have hit the quantization threshold error in level 1 and 0% of the cells have hit the quantization threshold error in level 2

5.2 Iteration 2:

Since, we are yet to achive atleast 80% compression at depth 2. Let’s try to compress again using the below mentioned set of model parameters and the data without novelty (containing 9522 records).

Model Parameters

Number of Cells at each Level = 30
Maximum Depth = 2
Quantization Error Threshold = 0.1
Error Metric = Max
Distance Metric = Manhattan

torus_mapC <- list()
torus_mapC <- trainHVT(data_without_novelty,
                  n_cells = 30,    
                  depth = 2,
                  quant.err = 0.1,
                  projection.scale = 10,
                  normalize = FALSE,
                  distance_metric = "L1_Norm",
                  error_metric = "max",
                  quant_method = "kmeans",
                  diagnose = FALSE,
                  scale_summary = mapA_scale_summary)

The datatable displayed below is the summary from map C (layer2). showing Cell.ID, Centroids and Quantization Error for each of the 924 cells.

summaryTable(torus_mapC[[3]]$summary,scroll = TRUE,limit = 500)

Segment.Level	Segment.Parent	Segment.Child	n	Cell.ID	Quant.Error	x	y	z
1	1	1	273	224	0.54	-1.43	1.97	0.75
1	1	2	392	508	0.48	1.33	-0.76	-0.81
1	1	3	353	397	0.45	1.03	0.21	0.09
1	1	4	358	342	0.5	-0.84	1.19	-0.76
1	1	5	300	802	0.54	-1.59	-1.47	-0.87
1	1	6	395	287	0.56	0.55	1.02	-0.47
1	1	7	344	710	0.43	-0.45	-1.52	0.81
1	1	8	291	728	0.65	-1.98	-0.82	0.87
1	1	9	371	559	0.48	-1.49	-0.03	-0.80
1	1	10	289	160	0.53	2.40	0.81	0.65
1	1	11	367	556	0.51	0.60	-0.93	0.36
1	1	12	287	391	0.55	-2.36	1.35	-0.44
1	1	13	343	175	0.61	2.00	0.97	-0.83
1	1	14	275	368	0.54	2.72	-0.33	-0.39
1	1	15	292	81	0.61	0.58	2.32	-0.77
1	1	16	252	123	0.55	-0.94	2.48	-0.58
1	1	17	283	491	0.56	-2.13	0.66	0.84
1	1	18	268	100	0.58	-0.03	2.42	0.74
1	1	19	264	776	0.57	0.84	-2.23	-0.78
1	1	20	274	766	0.54	-2.73	-0.50	-0.34
1	1	21	299	763	0.58	0.79	-2.25	0.78
1	1	22	249	29	0.57	1.59	2.29	0.31
1	1	23	328	228	0.43	0.90	1.22	0.83
1	1	24	205	873	0.58	-1.65	-2.12	0.52
1	1	25	444	655	0.53	-0.26	-1.17	-0.52
1	1	26	270	676	0.55	2.20	-1.75	0.10
1	1	27	262	881	0.53	-0.57	-2.70	-0.28
1	1	28	483	536	0.47	-1.03	-0.14	0.30
1	1	29	314	459	0.52	1.79	-0.57	0.90
1	1	30	397	350	0.48	-0.51	1.04	0.50
2	1	1	3	195	0.04	-0.72	1.95	1.00
2	1	2	6	366	0.04	-1.56	1.28	1.00
2	1	3	13	182	0.18	-2.02	2.19	0.14
2	1	4	12	249	0.12	-1.73	1.85	0.84
2	1	5	13	236	0.13	-2.10	1.92	0.52
2	1	6	4	339	0.05	-1.71	1.43	0.97
2	1	7	11	296	0.06	-1.85	1.61	0.89
2	1	8	5	242	0.06	-1.12	1.76	0.99
2	1	9	12	191	0.12	-1.68	2.15	0.68
2	1	10	16	284	0.08	-1.54	1.60	0.97
2	1	11	17	231	0.09	-1.42	1.92	0.92
2	1	12	11	286	0.08	-2.07	1.65	0.76
2	1	13	5	129	0.07	-1.10	2.47	0.71
2	1	14	13	137	0.08	-1.56	2.43	0.45
2	1	15	10	173	0.16	-1.86	2.26	0.36
2	1	16	6	270	0.07	-0.95	1.54	0.98
2	1	17	13	108	0.08	-1.35	2.62	0.32
2	1	18	6	92	0.03	-0.96	2.69	0.52
2	1	19	8	134	0.08	-0.86	2.40	0.83
2	1	20	13	202	0.08	-1.18	2.02	0.94
2	1	21	10	323	0.06	-1.29	1.38	0.99
2	1	22	5	186	0.08	-0.92	2.07	0.96
2	1	23	9	170	0.06	-1.44	2.27	0.72
2	1	24	4	357	0.01	-1.25	1.21	0.97
2	1	25	4	136	0.07	-1.33	2.44	0.62
2	1	26	13	282	0.06	-1.14	1.52	0.99
2	1	27	7	165	0.06	-1.00	2.23	0.89
2	1	28	10	218	0.04	-0.90	1.85	1.00
2	1	29	7	95	0.07	-1.11	2.68	0.42
2	1	30	7	217	0.04	-0.69	1.79	1.00
2	2	1	17	619	0.09	1.19	-1.36	-0.97
2	2	2	17	645	0.13	1.63	-1.52	-0.97
2	2	3	16	500	0.09	0.90	-0.58	-0.38
2	2	4	14	489	0.08	2.05	-0.74	-0.98
2	2	5	11	463	0.07	1.63	-0.48	-0.95
2	2	6	9	474	0.06	1.05	-0.38	-0.46
2	2	7	8	389	0.08	1.75	-0.03	-0.97
2	2	8	11	562	0.08	1.11	-1.06	-0.88
2	2	9	10	388	0.06	1.51	0.08	-0.87
2	2	10	12	579	0.08	0.63	-1.04	-0.62
2	2	11	10	466	0.08	1.93	-0.58	-1.00
2	2	12	6	429	0.05	1.58	-0.20	-0.91
2	2	13	12	560	0.07	1.35	-1.10	-0.96
2	2	14	23	561	0.13	2.00	-1.21	-0.93
2	2	15	14	543	0.07	0.73	-0.85	-0.47
2	2	16	10	475	0.07	1.18	-0.42	-0.66
2	2	17	16	533	0.06	1.03	-0.83	-0.74
2	2	18	14	497	0.08	1.23	-0.62	-0.78
2	2	19	13	521	0.08	1.43	-0.83	-0.94
2	2	20	20	615	0.1	0.75	-1.25	-0.84
2	2	21	9	420	0.08	1.38	-0.08	-0.78
2	2	22	17	487	0.07	1.44	-0.57	-0.89
2	2	23	8	445	0.06	1.31	-0.24	-0.74
2	2	24	11	425	0.08	1.90	-0.31	-0.99
2	2	25	15	515	0.09	1.68	-0.84	-0.99
2	2	26	19	504	0.09	1.02	-0.64	-0.61
2	2	27	12	592	0.08	1.57	-1.29	-1.00
2	2	28	9	447	0.04	1.45	-0.30	-0.85
2	2	29	14	554	0.08	0.82	-0.94	-0.65
2	2	30	15	448	0.06	1.16	-0.21	-0.57
2	3	1	9	341	0.06	1.06	0.51	0.57
2	3	2	14	353	0.08	0.83	0.57	0.10
2	3	3	11	332	0.07	0.87	0.65	0.40
2	3	4	13	371	0.08	0.90	0.44	-0.10
2	3	5	9	465	0.09	1.02	-0.34	0.39
2	3	6	12	377	0.06	1.03	0.32	0.38
2	3	7	13	407	0.07	1.03	0.12	0.25
2	3	8	9	370	0.07	1.03	0.40	-0.44
2	3	9	14	406	0.06	0.99	0.15	-0.02
2	3	10	14	367	0.06	1.18	0.35	-0.64
2	3	11	13	326	0.06	0.70	0.75	0.21
2	3	12	10	436	0.08	1.01	-0.08	0.14
2	3	13	7	426	0.06	1.01	0.00	-0.16
2	3	14	14	362	0.07	0.92	0.50	-0.30
2	3	15	16	456	0.08	0.99	-0.25	0.21
2	3	16	11	434	0.06	1.12	-0.08	-0.48
2	3	17	10	457	0.07	1.00	-0.24	-0.22
2	3	18	10	472	0.08	0.94	-0.34	-0.02
2	3	19	17	363	0.08	1.17	0.33	0.62
2	3	20	13	385	0.06	0.99	0.32	-0.28
2	3	21	14	349	0.06	0.96	0.51	0.41
2	3	22	6	435	0.03	1.05	-0.08	-0.32
2	3	23	7	409	0.03	1.04	0.12	-0.31
2	3	24	12	403	0.07	1.27	0.01	0.68
2	3	25	10	432	0.09	1.11	-0.10	0.46
2	3	26	13	402	0.07	1.15	0.12	-0.54
2	3	27	14	338	0.09	1.35	0.35	0.80
2	3	28	14	378	0.07	0.94	0.36	0.12
2	3	29	17	398	0.06	1.12	0.14	0.48
2	3	30	7	372	0.05	1.31	0.25	-0.75
2	4	1	14	374	0.1	-0.92	1.03	-0.78
2	4	2	14	369	0.07	-0.69	1.00	-0.62
2	4	3	15	289	0.08	-0.86	1.41	-0.93
2	4	4	6	239	0.07	-0.19	1.53	-0.89
2	4	5	13	290	0.08	-1.11	1.47	-0.98
2	4	6	10	216	0.06	-0.66	1.80	-0.99
2	4	7	10	300	0.06	-0.37	1.24	-0.71
2	4	8	21	356	0.08	-0.38	0.98	-0.33
2	4	9	21	430	0.09	-1.31	0.86	-0.90
2	4	10	15	359	0.09	-1.44	1.28	-0.99
2	4	11	9	314	0.07	-0.24	1.14	-0.55
2	4	12	11	337	0.07	-0.47	1.11	-0.60
2	4	13	12	223	0.06	-0.49	1.69	-0.97
2	4	14	10	443	0.07	-0.86	0.59	-0.27
2	4	15	13	277	0.07	-0.51	1.38	-0.85
2	4	16	4	266	0.05	-0.16	1.36	-0.77
2	4	17	11	329	0.08	-0.68	1.19	-0.78
2	4	18	4	215	0.02	-0.14	1.65	-0.94
2	4	19	13	419	0.09	-1.57	1.01	-0.99
2	4	20	7	417	0.07	-0.72	0.73	-0.25
2	4	21	12	386	0.06	-0.61	0.90	-0.40
2	4	22	8	254	0.1	-1.25	1.71	-0.99
2	4	23	15	424	0.09	-1.07	0.79	-0.74
2	4	24	16	418	0.09	-0.83	0.77	-0.49
2	4	25	15	245	0.07	-0.92	1.69	-0.99
2	4	26	11	450	0.08	-0.96	0.58	-0.47
2	4	27	10	258	0.06	-0.65	1.54	-0.94
2	4	28	16	297	0.09	-1.52	1.54	-0.98
2	4	29	8	201	0.07	-0.33	1.78	-0.98
2	4	30	14	358	0.1	-1.02	1.16	-0.89
2	5	1	9	716	0.09	-1.02	-1.17	-0.90
2	5	2	14	837	0.14	-0.99	-2.05	-0.96
2	5	3	7	820	0.07	-1.09	-1.84	-0.99
2	5	4	3	912	0.07	-1.80	-2.26	-0.45
2	5	5	4	793	0.04	-0.77	-1.76	-1.00
2	5	6	10	675	0.08	-1.12	-0.89	-0.82
2	5	7	9	816	0.07	-2.05	-1.25	-0.91
2	5	8	14	774	0.05	-1.74	-1.16	-0.99
2	5	9	6	681	0.06	-1.27	-0.83	-0.87
2	5	10	10	770	0.09	-0.95	-1.56	-0.98
2	5	11	12	801	0.06	-1.41	-1.52	-1.00
2	5	12	12	889	0.11	-2.27	-1.75	-0.49
2	5	13	8	806	0.05	-1.76	-1.36	-0.97
2	5	14	12	862	0.11	-2.36	-1.48	-0.61
2	5	15	8	845	0.1	-2.27	-1.38	-0.75
2	5	16	16	861	0.11	-1.39	-2.06	-0.87
2	5	17	10	850	0.09	-2.00	-1.59	-0.83
2	5	18	13	895	0.12	-2.06	-1.95	-0.53
2	5	19	10	834	0.08	-1.62	-1.70	-0.93
2	5	20	9	767	0.05	-1.48	-1.26	-1.00
2	5	21	9	747	0.05	-1.91	-0.81	-1.00
2	5	22	13	817	0.09	-1.29	-1.72	-0.98
2	5	23	11	758	0.07	-1.13	-1.37	-0.97
2	5	24	13	732	0.07	-1.67	-0.89	-0.99
2	5	25	6	887	0.07	-1.55	-2.23	-0.70
2	5	26	15	743	0.07	-1.33	-1.15	-0.97
2	5	27	10	717	0.08	-1.44	-0.93	-0.96
2	5	28	13	871	0.09	-1.81	-1.92	-0.76
2	5	29	6	772	0.05	-1.94	-1.01	-0.98
2	5	30	8	811	0.08	-2.23	-1.09	-0.87
2	6	1	11	319	0.05	0.57	0.84	0.19
2	6	2	13	291	0.05	0.37	1.06	-0.48
2	6	3	10	317	0.07	0.32	0.95	-0.01
2	6	4	20	322	0.1	-0.07	1.05	-0.31
2	6	5	9	226	0.08	0.15	1.51	-0.87
2	6	6	8	312	0.06	0.34	0.96	0.21
2	6	7	14	313	0.07	0.25	1.00	-0.24
2	6	8	6	192	0.06	0.75	1.48	-0.94
2	6	9	10	179	0.08	1.10	1.43	-0.98
2	6	10	21	255	0.09	1.10	0.98	-0.85
2	6	11	17	335	0.07	0.85	0.66	-0.38
2	6	12	23	304	0.08	0.72	0.87	-0.48
2	6	13	14	324	0.07	0.05	1.00	-0.07
2	6	14	19	331	0.08	0.70	0.74	-0.18
2	6	15	16	260	0.06	0.37	1.24	-0.70
2	6	16	15	294	0.08	0.17	1.12	-0.49
2	6	17	16	301	0.08	0.93	0.79	-0.63
2	6	18	14	321	0.1	1.10	0.61	-0.67
2	6	19	15	293	0.07	0.52	1.00	-0.48
2	6	20	6	207	0.05	0.44	1.52	-0.91
2	6	21	12	275	0.11	0.00	1.27	-0.68
2	6	22	15	222	0.09	0.86	1.28	-0.89
2	6	23	15	248	0.1	0.92	1.12	-0.83
2	6	24	10	238	0.06	0.58	1.31	-0.82
2	6	25	12	318	0.04	0.22	0.98	0.12
2	6	26	10	265	0.08	0.74	1.08	-0.72
2	6	27	6	316	0.05	0.49	0.89	0.13
2	6	28	17	311	0.07	0.47	0.91	-0.23
2	6	29	12	325	0.08	0.60	0.80	-0.04
2	6	30	9	250	0.06	0.22	1.35	-0.78
2	7	1	14	786	0.08	-0.08	-2.10	0.99
2	7	2	10	618	0.08	-0.31	-1.00	0.31
2	7	3	8	627	0.04	-0.46	-0.98	0.40
2	7	4	13	701	0.08	-0.67	-1.36	0.87
2	7	5	8	629	0.06	-0.37	-1.05	0.46
2	7	6	10	651	0.06	-0.58	-1.09	0.64
2	7	7	11	630	0.06	-0.70	-0.92	0.53
2	7	8	11	637	0.08	-0.10	-1.17	0.56
2	7	9	11	740	0.08	-0.74	-1.55	0.96
2	7	10	14	807	0.08	-0.37	-2.14	0.98
2	7	11	9	726	0.07	-0.49	-1.57	0.93
2	7	12	11	683	0.08	0.24	-1.53	0.89
2	7	13	5	662	0.05	-0.18	-1.30	0.73
2	7	14	10	697	0.07	-0.06	-1.54	0.89
2	7	15	17	847	0.14	-0.45	-2.47	0.85
2	7	16	12	647	0.05	-0.29	-1.17	0.60
2	7	17	15	764	0.08	-0.50	-1.81	0.99
2	7	18	8	698	0.12	-1.15	-1.11	0.91
2	7	19	11	833	0.09	-0.72	-2.24	0.93
2	7	20	14	731	0.08	0.11	-1.80	0.98
2	7	21	10	690	0.06	-0.37	-1.37	0.81
2	7	22	4	613	0.02	-0.53	-0.90	0.30
2	7	23	14	749	0.09	-0.21	-1.78	0.97
2	7	24	15	771	0.1	-1.00	-1.67	1.00
2	7	25	11	688	0.06	-0.13	-1.44	0.83
2	7	26	10	815	0.09	-0.96	-1.97	0.98
2	7	27	17	657	0.09	-0.81	-1.03	0.72
2	7	28	14	648	0.07	0.07	-1.30	0.71
2	7	29	8	660	0.06	-0.50	-1.18	0.69
2	7	30	19	729	0.13	-1.03	-1.36	0.95
2	8	1	11	667	0.09	-1.56	-0.66	0.95
2	8	2	3	622	0.02	-1.95	-0.20	1.00
2	8	3	17	829	0.1	-2.14	-1.41	0.82
2	8	4	15	788	0.09	-2.28	-1.01	0.87
2	8	5	11	711	0.07	-1.43	-1.02	0.97
2	8	6	9	585	0.08	-1.63	-0.19	0.93
2	8	7	8	754	0.07	-2.58	-0.55	0.77
2	8	8	14	663	0.07	-1.77	-0.51	0.99
2	8	9	8	635	0.03	-1.85	-0.31	0.99
2	8	10	10	666	0.06	-2.02	-0.40	1.00
2	8	11	8	782	0.08	-1.93	-1.24	0.95
2	8	12	8	703	0.07	-1.67	-0.81	0.99
2	8	13	7	735	0.06	-1.68	-1.03	1.00
2	8	14	16	859	0.15	-2.48	-1.42	0.48
2	8	15	7	762	0.04	-1.54	-1.31	1.00
2	8	16	11	739	0.07	-1.35	-1.23	0.98
2	8	17	17	671	0.1	-1.22	-0.90	0.87
2	8	18	14	699	0.07	-2.51	-0.28	0.85
2	8	19	15	810	0.09	-2.44	-1.05	0.75
2	8	20	7	751	0.07	-2.07	-0.88	0.97
2	8	21	5	750	0.04	-1.89	-0.97	0.99
2	8	22	6	804	0.09	-2.65	-0.82	0.62
2	8	23	8	794	0.07	-1.73	-1.40	0.97
2	8	24	8	738	0.08	-2.69	-0.35	0.69
2	8	25	4	589	0.03	-1.81	-0.11	0.98
2	8	26	7	842	0.1	-2.64	-1.16	0.45
2	8	27	8	665	0.07	-2.24	-0.27	0.96
2	8	28	11	623	0.1	-1.43	-0.51	0.88
2	8	29	10	730	0.12	-2.31	-0.60	0.91
2	8	30	8	702	0.07	-2.00	-0.63	0.99
2	9	1	10	473	0.06	-1.70	0.71	-0.98
2	9	2	17	673	0.08	-2.05	-0.28	-0.99
2	9	3	20	513	0.1	-1.13	0.13	-0.50
2	9	4	16	478	0.1	-1.42	0.57	-0.88
2	9	5	14	541	0.07	-1.31	-0.01	-0.73
2	9	6	16	563	0.08	-1.98	0.21	-1.00
2	9	7	11	575	0.09	-1.06	-0.38	-0.48
2	9	8	18	520	0.08	-1.36	0.21	-0.78
2	9	9	11	510	0.08	-1.65	0.40	-0.95
2	9	10	15	546	0.08	-1.63	0.14	-0.93
2	9	11	8	616	0.06	-2.06	-0.01	-1.00
2	9	12	16	631	0.08	-1.21	-0.58	-0.75
2	9	13	19	548	0.09	-1.13	-0.17	-0.50
2	9	14	20	567	0.08	-1.52	-0.07	-0.88
2	9	15	18	481	0.1	-1.17	0.41	-0.64
2	9	16	10	708	0.06	-2.00	-0.54	-1.00
2	9	17	9	658	0.05	-1.58	-0.49	-0.94
2	9	18	16	626	0.09	-1.06	-0.64	-0.65
2	9	19	9	569	0.06	-1.24	-0.25	-0.67
2	9	20	11	661	0.05	-1.45	-0.59	-0.90
2	9	21	9	612	0.06	-1.78	-0.14	-0.98
2	9	22	20	486	0.08	-1.03	0.32	-0.40
2	9	23	9	572	0.09	-2.30	0.27	-0.95
2	9	24	15	600	0.08	-1.39	-0.34	-0.82
2	9	25	10	693	0.05	-1.75	-0.58	-0.99
2	9	26	8	638	0.03	-1.64	-0.34	-0.95
2	9	27	16	505	0.09	-1.89	0.52	-1.00
2	9	28	0	NA	NA	NA	NA	NA
2	9	29	0	NA	NA	NA	NA	NA
2	9	30	0	NA	NA	NA	NA	NA
2	10	1	11	267	0.08	1.87	0.41	0.99
2	10	2	13	227	0.11	1.73	0.74	0.99
2	10	3	7	51	0.09	2.61	1.37	0.31
2	10	4	5	118	0.05	2.92	0.68	0.02
2	10	5	8	142	0.05	1.83	1.20	0.98
2	10	6	5	141	0.08	2.73	0.66	0.58
2	10	7	7	72	0.1	2.53	1.24	0.57
2	10	8	12	219	0.08	2.10	0.58	0.98
2	10	9	8	190	0.06	1.98	0.83	0.99
2	10	10	11	110	0.08	2.79	0.85	0.39
2	10	11	12	177	0.06	1.78	1.02	1.00
2	10	12	14	53	0.1	2.71	1.27	-0.01
2	10	13	9	73	0.09	2.69	1.12	0.39
2	10	14	10	184	0.09	2.56	0.55	0.78
2	10	15	16	243	0.11	2.49	0.23	0.86
2	10	16	9	96	0.11	1.93	1.50	0.89
2	10	17	5	163	0.05	2.91	0.44	0.33
2	10	18	11	198	0.08	2.80	0.29	0.57
2	10	19	10	268	0.07	2.12	0.28	0.99
2	10	20	17	56	0.11	2.28	1.57	0.63
2	10	21	8	153	0.06	2.09	1.02	0.94
2	10	22	7	117	0.06	2.04	1.27	0.91
2	10	23	7	187	0.06	2.93	0.30	0.32
2	10	24	13	113	0.12	2.46	1.05	0.74
2	10	25	8	156	0.07	2.32	0.85	0.88
2	10	26	6	204	0.07	2.31	0.54	0.93
2	10	27	12	74	0.1	2.81	1.04	0.09
2	10	28	6	90	0.07	2.84	0.90	-0.19
2	10	29	7	138	0.05	2.93	0.56	0.18
2	10	30	15	256	0.14	2.70	0.07	0.70
2	11	1	11	607	0.07	0.40	-1.20	0.67
2	11	2	8	640	0.05	0.55	-1.39	0.86
2	11	3	9	584	0.06	0.38	-1.04	0.45
2	11	4	14	535	0.07	0.80	-0.82	0.52
2	11	5	15	484	0.06	1.02	-0.49	0.50
2	11	6	9	621	0.09	0.74	-1.33	0.88
2	11	7	15	566	0.1	0.39	-0.92	0.00
2	11	8	11	564	0.06	0.44	-0.92	0.22
2	11	9	7	605	0.06	0.21	-1.13	0.52
2	11	10	14	588	0.06	0.18	-0.98	0.00
2	11	11	13	587	0.06	0.22	-1.01	0.24
2	11	12	10	576	0.05	0.82	-1.13	0.79
2	11	13	12	551	0.06	0.59	-0.89	0.37
2	11	14	13	506	0.08	1.02	-0.72	0.66
2	11	15	15	608	0.08	-0.10	-1.03	0.27
2	11	16	10	568	0.06	0.61	-1.02	0.59
2	11	17	15	542	0.08	0.57	-0.82	0.05
2	11	18	17	582	0.08	1.04	-1.24	0.92
2	11	19	9	601	0.06	0.56	-1.21	0.75
2	11	20	18	503	0.11	0.81	-0.59	-0.04
2	11	21	12	526	0.08	0.75	-0.70	-0.22
2	11	22	15	496	0.08	0.88	-0.54	0.24
2	11	23	14	550	0.08	0.87	-0.98	0.72
2	11	24	9	511	0.07	0.86	-0.67	0.41
2	11	25	12	532	0.07	0.71	-0.73	0.20
2	11	26	5	632	0.03	0.21	-1.25	0.68
2	11	27	6	537	0.06	1.07	-0.92	0.81
2	11	28	10	603	0.04	0.06	-1.06	0.35
2	11	29	9	652	0.07	0.36	-1.40	0.83
2	11	30	30	552	0.09	0.57	-0.87	-0.28
2	12	1	6	292	0.06	-2.45	1.66	-0.28
2	12	2	12	344	0.08	-1.97	1.46	-0.89
2	12	3	7	364	0.08	-2.60	1.48	-0.11
2	12	4	9	283	0.06	-2.48	1.67	0.03
2	12	5	5	247	0.05	-2.34	1.87	0.05
2	12	6	7	455	0.09	-2.26	0.98	-0.89
2	12	7	10	211	0.08	-1.91	2.07	-0.57
2	12	8	12	237	0.09	-2.18	1.92	-0.42
2	12	9	5	387	0.05	-1.75	1.25	-0.99
2	12	10	17	470	0.12	-2.80	1.02	-0.18
2	12	11	7	309	0.08	-2.17	1.60	-0.71
2	12	12	10	444	0.12	-1.87	0.95	-0.99
2	12	13	15	393	0.09	-2.29	1.33	-0.76
2	12	14	11	498	0.08	-2.47	0.79	-0.80
2	12	15	12	528	0.13	-2.73	0.72	-0.55
2	12	16	8	274	0.08	-1.74	1.71	-0.89
2	12	17	11	530	0.12	-2.90	0.72	-0.12
2	12	18	12	307	0.11	-2.37	1.62	-0.49
2	12	19	7	452	0.09	-2.76	1.12	0.17
2	12	20	10	261	0.09	-1.93	1.79	-0.77
2	12	21	8	423	0.08	-2.12	1.12	-0.91
2	12	22	5	544	0.09	-2.57	0.52	-0.78
2	12	23	5	253	0.07	-2.32	1.82	0.31
2	12	24	10	519	0.06	-2.30	0.60	-0.93
2	12	25	14	354	0.11	-2.55	1.49	0.29
2	12	26	6	259	0.08	-2.39	1.79	-0.17
2	12	27	13	400	0.09	-2.68	1.34	0.04
2	12	28	8	209	0.08	-2.18	2.05	-0.01
2	12	29	20	439	0.12	-2.60	1.17	-0.52
2	12	30	5	183	0.08	-2.00	2.19	-0.24
2	13	1	9	85	0.09	2.57	1.11	-0.59
2	13	2	14	149	0.09	1.37	1.47	-0.99
2	13	3	8	157	0.06	2.14	0.94	-0.94
2	13	4	20	97	0.1	1.67	1.62	-0.94
2	13	5	13	49	0.09	2.53	1.43	-0.41
2	13	6	9	169	0.08	2.44	0.67	-0.84
2	13	7	18	285	0.11	1.32	0.65	-0.85
2	13	8	9	220	0.08	1.31	1.07	-0.95
2	13	9	8	67	0.06	2.42	1.32	-0.65
2	13	10	9	30	0.11	2.31	1.75	-0.43
2	13	11	11	88	0.1	2.76	0.98	-0.36
2	13	12	18	246	0.09	1.48	0.82	-0.95
2	13	13	14	124	0.12	1.99	1.24	-0.93
2	13	14	16	272	0.08	1.69	0.53	-0.97
2	13	15	11	154	0.08	2.69	0.62	-0.64
2	13	16	15	196	0.07	1.88	0.85	-1.00
2	13	17	12	333	0.1	1.55	0.31	-0.91
2	13	18	8	87	0.07	2.16	1.38	-0.82
2	13	19	8	197	0.09	2.10	0.70	-0.97
2	13	20	17	230	0.08	2.29	0.41	-0.94
2	13	21	6	50	0.09	2.16	1.64	-0.69
2	13	22	14	125	0.12	2.41	0.97	-0.80
2	13	23	10	279	0.07	2.13	0.22	-0.99
2	13	24	9	340	0.08	1.85	0.14	-0.99
2	13	25	14	42	0.13	1.93	1.86	-0.71
2	13	26	5	45	0.1	2.63	1.38	-0.21
2	13	27	6	206	0.08	2.49	0.43	-0.85
2	13	28	10	264	0.08	1.88	0.44	-0.99
2	13	29	13	178	0.11	1.59	1.16	-1.00
2	13	30	9	103	0.08	2.29	1.21	-0.81
2	14	1	6	234	0.08	2.99	0.02	-0.05
2	14	2	9	516	0.07	2.76	-1.12	-0.21
2	14	3	18	306	0.12	2.60	-0.11	-0.79
2	14	4	7	431	0.06	2.90	-0.69	0.18
2	14	5	7	461	0.11	2.87	-0.86	-0.06
2	14	6	9	525	0.06	2.45	-1.06	-0.74
2	14	7	16	241	0.12	2.62	0.19	-0.77
2	14	8	3	233	0.06	2.94	0.07	0.32
2	14	9	5	280	0.05	2.94	-0.19	0.33
2	14	10	9	139	0.07	2.92	0.55	-0.21
2	14	11	4	167	0.06	2.97	0.36	0.04
2	14	12	9	438	0.08	2.80	-0.70	0.46
2	14	13	8	468	0.06	2.82	-0.89	0.27
2	14	14	7	181	0.07	2.95	0.32	-0.25
2	14	15	20	276	0.09	2.90	-0.14	-0.42
2	14	16	10	373	0.12	2.20	-0.16	-0.97
2	14	17	8	383	0.08	2.93	-0.50	0.24
2	14	18	11	483	0.08	2.59	-0.84	-0.69
2	14	19	13	480	0.08	2.36	-0.79	-0.87
2	14	20	11	288	0.08	2.34	0.06	-0.94
2	14	21	7	509	0.09	2.66	-1.08	-0.48
2	14	22	5	252	0.01	2.98	-0.06	0.19
2	14	23	7	404	0.1	2.64	-0.45	-0.73
2	14	24	5	336	0.09	2.87	-0.32	0.45
2	14	25	10	390	0.12	2.88	-0.48	-0.38
2	14	26	10	437	0.09	2.33	-0.52	-0.92
2	14	27	10	166	0.07	2.83	0.44	-0.50
2	14	28	10	232	0.12	2.88	0.10	-0.46
2	14	29	10	454	0.09	2.81	-0.77	-0.40
2	14	30	11	330	0.09	2.97	-0.35	-0.05
2	15	1	11	78	0.06	1.04	2.09	-0.94
2	15	2	12	68	0.1	1.34	2.00	-0.91
2	15	3	15	39	0.13	0.63	2.64	-0.69
2	15	4	5	185	0.06	0.44	1.66	-0.96
2	15	5	6	13	0.1	0.56	2.94	-0.04
2	15	6	13	10	0.1	0.89	2.84	-0.20
2	15	7	7	34	0.05	1.43	2.30	-0.70
2	15	8	11	62	0.09	0.42	2.51	-0.84
2	15	9	7	18	0.1	1.22	2.58	-0.51
2	15	10	13	143	0.06	0.97	1.68	-1.00
2	15	11	15	43	0.14	0.17	2.75	-0.65
2	15	12	10	63	0.1	0.91	2.30	-0.88
2	15	13	9	194	0.06	0.04	1.71	-0.96
2	15	14	12	36	0.09	1.21	2.40	-0.72
2	15	15	16	27	0.14	0.11	2.95	-0.29
2	15	16	6	111	0.07	0.96	1.92	-0.99
2	15	17	10	145	0.06	0.32	1.91	-0.99
2	15	18	5	91	0.08	-0.11	2.42	-0.90
2	15	19	13	64	0.07	0.02	2.62	-0.78
2	15	20	7	99	0.05	0.37	2.22	-0.97
2	15	21	6	105	0.06	1.15	1.86	-0.98
2	15	22	11	147	0.07	0.10	1.98	-1.00
2	15	23	8	86	0.07	0.63	2.22	-0.95
2	15	24	10	22	0.09	0.42	2.89	-0.37
2	15	25	8	132	0.06	0.56	1.91	-1.00
2	15	26	7	155	0.07	-0.19	2.02	-1.00
2	15	27	11	164	0.07	0.74	1.66	-0.98
2	15	28	8	120	0.06	0.04	2.16	-0.99
2	15	29	9	94	0.06	0.04	2.35	-0.93
2	15	30	11	24	0.11	0.96	2.65	-0.57
2	16	1	8	40	0.09	-0.21	2.92	-0.37
2	16	2	9	208	0.05	-1.23	1.99	-0.94
2	16	3	13	152	0.12	-1.78	2.34	-0.31
2	16	4	5	146	0.07	-1.19	2.37	-0.76
2	16	5	8	107	0.09	-1.12	2.61	-0.54
2	16	6	8	48	0.05	-0.57	2.94	0.05
2	16	7	12	60	0.11	-0.29	2.75	-0.63
2	16	8	8	148	0.11	-0.37	2.14	-0.98
2	16	9	8	109	0.1	-1.51	2.59	-0.03
2	16	10	7	61	0.08	-0.64	2.84	-0.41
2	16	11	6	225	0.06	-1.46	1.94	-0.90
2	16	12	12	76	0.08	-0.57	2.70	-0.65
2	16	13	8	162	0.1	-1.56	2.28	-0.64
2	16	14	7	188	0.08	-1.49	2.15	-0.79
2	16	15	6	47	0.07	-0.51	2.93	-0.22
2	16	16	4	210	0.03	-1.67	2.06	-0.75
2	16	17	9	93	0.09	-0.89	2.67	-0.58
2	16	18	7	65	0.09	-0.87	2.86	0.13
2	16	19	10	130	0.08	-1.53	2.45	-0.45
2	16	20	16	140	0.07	-0.92	2.32	-0.87

Now let’s check the compression summary for HVT (torus_mapC). The table below shows no of cells, no of cells having quantization error below threshold and percentage of cells having quantization error below threshold for each level.

mapC_compression_summary <- torus_mapC[[3]]$compression_summary %>%  dplyr::mutate_if(is.numeric, funs(round(.,4)))
compressionSummaryTable(mapC_compression_summary)

segmentLevel	noOfCells	noOfCellsBelowQuantizationError	percentOfCellsBelowQuantizationErrorThreshold	parameters
1	30	0	0	n_cells: 30 quant.err: 0.1 distance_metric: L1_Norm error_metric: max quant_method: kmeans
2	894	767	0.86	n_cells: 30 quant.err: 0.1 distance_metric: L1_Norm error_metric: max quant_method: kmeans

As it can be seen from the table above, 0% of the cells have hit the quantization threshold error in level 1 and 86% of the cells have hit the quantization threshold error in level 2

Let’s plot the Voronoi tessellation for layer 2 (map C)

plotHVT(torus_mapC,
        line.width = c(0.4,0.2), 
        color.vec = c("#141B41","#0582CA"),
        centroid.size = 0.1,
        maxDepth = 2, 
        heatmap = '2Dhvt')

Figure 14: The Voronoi Tessellation for layer 2 (map C) shown for the 924 cells in the dataset ’torus’ at level 2

Heat Maps

Now let’s plot all the features for each cell at level two as a heatmap for better visualization.


  plotHVT(
  torus_mapC,
  trainTorus_data,
  child.level = 2,
  hmap.cols = "x",
  line.width = c(0.6,0.4),
  color.vec = c("#141B41","#0582CA"),
  palette.color = 6,
  centroid.size = 0.1,
  show.points = TRUE,
  quant.error.hmap = 0.2,
  n_cells.hmap = 100,
  heatmap = '2Dheatmap'
)

Figure 15: The Voronoi Tessellation with the heat map overlaid for feature x in the ’torus’ dataset


  plotHVT(
  torus_mapC,
  trainTorus_data,
  child.level = 2,
  hmap.cols = "y",
  line.width = c(0.6,0.4),
  color.vec = c("#141B41","#0582CA"),
  palette.color = 6,
  centroid.size = 0.1,
  show.points = TRUE,
  quant.error.hmap = 0.2,
  n_cells.hmap = 100,
  heatmap = '2Dheatmap'
)

Figure 16: The Voronoi Tessellation with the heat map overlaid for feature y in the ’torus’ dataset


  plotHVT(
  torus_mapC,
  trainTorus_data,
  child.level = 2,
  hmap.cols = "z",
  line.width = c(0.6,0.4),
  color.vec = c("#141B41","#0582CA"),
  palette.color = 6,
  centroid.size = 0.1,
  show.points = TRUE,
  quant.error.hmap = 0.2,
  n_cells.hmap = 100,
  heatmap = '2Dheatmap'
)

Figure 17: The Voronoi Tessellation with the heat map overlaid for feature z in the ’torus’ dataset

We now have the set of maps (map A, map B & map C) which will be used to score, which map and cell each test record is assigned to, but before that lets view our test dataset

6. Scoring on Test Data

Now once we have built the model, let us try to score using our test dataset (containing 2400 data points) which cell and which layer each point belongs to.

Testing Dataset

The testing dataset includes the following columns:

x: This column represents the X-coordinate of each point in the torus.
y: This column represents the Y-coordinate of each point in the torus.
z: This column represents the Z-coordinate of each point in the torus.

Let’s have a look at our randomly selected test dataset containing 2400 datapoints.

Table(head(testTorus_data))

x	y	z
-1.8031	1.5092	0.9362
1.1817	-1.0655	-0.9126
0.9942	-1.2500	-0.9153
1.0669	-0.0514	-0.3627
0.5570	-0.8837	-0.2954
0.8776	-0.4958	-0.1259

The scoreLayeredHVT function is used to score the test data using the scored set of maps. This function takes an input - a test data and a set of maps (map A, map B, map C).

Now, Let us understand the scoreLayeredHVT function.

scoreLayeredHVT(data,
                map_A,
                map_B,
                map_C,
                mad.threshold = 0.2,
                normalize = TRUE, 
                distance_metric="L1_Norm",
                error_metric="max",
                child.level = 1, 
                line.width = c(0.6, 0.4, 0.2),
                color.vec = c("#141B41", "#6369D1", "#D8D2E1"),
                yVar= NULL,
                ...)

Each of the parameters of scoreLayeredHVT function has been explained below:

data - A dataframe containing the test dataset. The dataframe should have all the variable(features) used for training.
map A - Result (hvt.result) obtained from HVT function while performing hierarchical vector quantization on train data. This list containes information about the hierarchical vector quantized data along with a summary section.
map B - Result (hvt.result) obtained from HVT function while performing hierarchical vector quantization on novelty data. Novelty data is a subset of the training data obtained as a result of removeNovelty function (1st element).
map C - Result (hvt.result) obtained from HVT function while performing hierarchical vector quantization on training data without novelty. This data is a subset of the training data obtained as a result of removeNovelty function (2nd element).
child.level - A number indicating the depth for which the heat map is to be plotted (Only used if hmap.cols is not NULL), Each depth represents a different level of clustering or partitioning of the data.
mad.threshold - A threshold value used to filter data based on the Median Absolute Deviation (MAD) of the Quant.Error variable. It determines how extreme a deviation from the median has to be in order to consider as novelty
normalize - A logical value indicating if the dataset should be normalized. When set to TRUE, scales the values of all features to have a mean of 0 and a standard deviation of 1 (Z-score)
distance_metric - The distance metric can be L1_Norm(Manhattan) or L2_Norm(Eucledian). L1_Norm is selected by default. The distance metric is used to calculate the distance between an n dimensional point and centroid. The distance metric can be different from the one used during training.
error_metric - The error metric can be mean or max. max is selected by default. max will return the max of m values and mean will take mean of m values where each value is a distance between a point and centroid of the cell. The error metric can be different from the one used during training.
yVar - A character or a vector representing the name of the dependent variable(s)
line.width - A vector indicating the line widths of the tessellation boundaries for each layer. (Optional Parameters)
color.vec - A vector indicating the colors of the tessellations boundaries at each layer. (Optional Parameters)

The function score based on the HVT maps - map A, map B and map C, constructed using trainHVT function. For each test record, the function will assign that record to Layer1 or Layer2. Layer1 contains the cell ids from map A and Layer 2 contains cell ids from map B (novelty map) and map C (map without novelty).

Scoring Algorithm

The Scoring algorithm recursively calculates the distance between each point in the test dataset and the cell centroids for each level. The following steps explain the scoring method for a single point in the test dataset:

Calculate the distance between the point and the centroid of all the cells in the first level.
Find the cell whose centroid has minimum distance to the point.
Check if the cell drills down further to form more cells.
If it doesn’t, return the path. Or else repeat steps 1 to 4 till we reach a level at which the cell doesn’t drill down further.

Note : The Scoring algorithm will not work if some of the variables used to perform quantization are missing. In the test dataset, we should not remove any features


validation_data <- testTorus_data
new_score <- scoreLayeredHVT(
    data=validation_data,
    torus_mapA,
    torus_mapB,
    torus_mapC,
    normalize = FALSE
  )

Let’s see which cell and layer each point belongs to and check the Mean Absolute Difference for each of the 2400 records.


act_pred <- new_score[["actual_predictedTable"]]
rownames(act_pred) <- NULL
act_pred %>% head(1000) %>%as.data.frame() %>%Table(scroll = TRUE)

Row.Number	act_x	act_y	act_z	Layer1.Cell.ID	Layer2.Cell.ID	pred_x	pred_y	pred_z	diff
1	-1.8031	1.5092	0.9362	A115	C224	-1.4293520	1.9746821	0.7526839	0.3409154
2	1.1817	-1.0655	-0.9126	A670	C508	1.3298237	-0.7586967	-0.8086783	0.1862829
3	0.9942	-1.2500	-0.9153	A637	C508	1.3298237	-0.7586967	-0.8086783	0.3111829
4	1.0669	-0.0514	-0.3627	A629	C397	1.0336915	0.2140921	0.0921008	0.2511671
5	0.5570	-0.8837	-0.2954	A560	C556	0.6025305	-0.9291853	0.3583787	0.2482649
6	0.8776	-0.4958	-0.1259	A601	C397	1.0336915	0.2140921	0.0921008	0.3613281
7	-2.3233	-0.7173	0.9021	A93	C728	-1.9816416	-0.8223302	0.8717976	0.1589970
8	-1.4379	-1.4182	-0.9998	A201	C802	-1.5935443	-1.4685237	-0.8727753	0.1109976
9	-1.1262	0.4838	-0.6328	A286	C559	-1.4876296	-0.0265439	-0.7952792	0.3447509
10	-0.1641	0.9975	-0.1472	A422	C350	-0.5144181	1.0433207	0.4973778	0.3469055
11	0.9033	-1.7767	1.0000	A705	C763	0.7912866	-2.2489217	0.7766609	0.2691914
12	2.2775	-0.0413	-0.9606	A815	C368	2.7225869	-0.3304495	-0.3889044	0.4353107
13	1.0593	-0.8066	-0.7437	A652	C508	1.3298237	-0.7586967	-0.8086783	0.1278018
14	1.4834	0.4428	0.8920	A685	C459	1.7910516	-0.5739146	0.9028013	0.4450558
15	0.2045	1.1079	-0.4871	A479	C287	0.5468719	1.0211322	-0.4670886	0.1497170
16	2.2440	-1.5745	-0.6712	A873	C676	2.1950559	-1.7495404	0.0972307	0.3308051
17	-0.9745	2.8003	0.2623	A192	C123	-0.9422671	2.4806302	-0.5791599	0.3977876
18	0.5850	0.8331	-0.1890	A532	C287	0.5468719	1.0211322	-0.4670886	0.1680830
19	-1.5044	2.3446	0.6185	A135	C224	-1.4293520	1.9746821	0.7526839	0.1930499
20	1.5809	-0.4652	0.9360	A748	C459	1.7910516	-0.5739146	0.9028013	0.1173550
21	-1.9374	-2.2744	-0.1564	A109	C873	-1.6544946	-2.1236132	0.5230898	0.3710607
22	-0.8860	0.6243	0.4009	A333	C350	-0.5144181	1.0433207	0.4973778	0.2956935
23	0.9783	2.2893	-0.8720	A674	C81	0.5783356	2.3154644	-0.7661384	0.1773301
24	0.8406	2.1602	-0.9481	A674	C81	0.5783356	2.3154644	-0.7661384	0.1998301
25	0.4730	2.9532	0.1347	A558	C100	-0.0270481	2.4238631	0.7389638	0.5445496
26	-0.5176	-0.8570	-0.0496	A393	C655	-0.2597926	-1.1730025	-0.5212327	0.3484809
27	2.4540	-1.0923	-0.7275	A854	C368	2.7225869	-0.3304495	-0.3889044	0.4563444
28	2.2682	1.9181	-0.2412	A848	B1	2.2784556	1.9447222	0.0217667	0.0999481
29	2.5442	-1.4977	-0.3052	A882	C676	2.1950559	-1.7495404	0.0972307	0.3344717
30	0.0410	1.0727	-0.3763	A479	C287	0.5468719	1.0211322	-0.4670886	0.2160761
31	-0.8827	-0.7320	-0.5215	A359	C655	-0.2597926	-1.1730025	-0.5212327	0.3547258
32	-2.2024	-0.7311	0.9472	A93	C728	-1.9816416	-0.8223302	0.8717976	0.1291304
33	-2.3576	1.3298	0.7075	A40	C491	-2.1349643	0.6623576	0.8377438	0.3401073
34	0.9179	0.7176	-0.5504	A608	C287	0.5468719	1.0211322	-0.4670886	0.2526239
35	0.4195	-0.9159	0.1218	A525	C556	0.6025305	-0.9291853	0.3583787	0.1442982
36	1.5297	1.9185	-0.8912	A723	C175	1.9954496	0.9735682	-0.8296280	0.4907511
37	-0.1005	-0.9954	-0.0290	A448	C655	-0.2597926	-1.1730025	-0.5212327	0.2763759
38	1.7796	0.1579	-0.9770	A749	C175	1.9954496	0.9735682	-0.8296280	0.3929633
39	2.0152	1.8853	0.6504	A803	C29	1.5896815	2.2890353	0.3101313	0.3898408
40	-0.8793	-1.8737	0.9976	A269	C710	-0.4532110	-1.5200102	0.8113151	0.3220212
41	0.4925	-2.4521	-0.8654	A673	C776	0.8378659	-2.2297098	-0.7821201	0.2170120
42	1.5076	-1.4888	-0.9929	A768	C508	1.3298237	-0.7586967	-0.8086783	0.3640338
43	0.9571	2.7347	0.4413	A700	C29	1.5896815	2.2890353	0.3101313	0.4031383
44	1.6536	-0.9304	-0.9947	A751	C508	1.3298237	-0.7586967	-0.8086783	0.2271671
45	1.7288	-0.7202	0.9919	A748	C459	1.7910516	-0.5739146	0.9028013	0.0992119
46	-1.3049	-0.9790	-0.9296	A230	C802	-1.5935443	-1.4685237	-0.8727753	0.2783309
47	0.3303	2.4880	0.8603	A488	C100	-0.0270481	2.4238631	0.7389638	0.1809404
48	-0.9228	-2.5717	0.6811	A340	C873	-1.6544946	-2.1236132	0.5230898	0.4459306
49	2.4008	0.4820	-0.8937	A802	C175	1.9954496	0.9735682	-0.8296280	0.3203302
50	1.2205	-2.0992	-0.9037	A740	C776	0.8378659	-2.2297098	-0.7821201	0.2115746
51	2.5423	0.7690	0.7547	A826	C160	2.3972612	0.8131370	0.6512993	0.0975255
52	2.7894	-0.6793	-0.4915	A888	C368	2.7225869	-0.3304495	-0.3889044	0.1727531
53	-1.5250	2.5695	0.1549	A99	C224	-1.4293520	1.9746821	0.7526839	0.4294166
54	1.1750	1.3937	0.9842	A635	C228	0.8994003	1.2236527	0.8271905	0.2008855
55	-2.1343	-1.4370	0.8195	A108	C728	-1.9816416	-0.8223302	0.8717976	0.2732086
56	0.4443	-1.0409	-0.4962	A542	C655	-0.2597926	-1.1730025	-0.5212327	0.2870759
57	-1.4290	0.1447	0.8260	A227	C536	-1.0323493	-0.1417128	0.3010375	0.4026754
58	-1.1483	0.6003	0.7099	A258	C491	-2.1349643	0.6623576	0.8377438	0.3921886
59	0.6935	1.5007	-0.9379	A582	C287	0.5468719	1.0211322	-0.4670886	0.3656691
60	-1.6762	0.3047	-0.9551	A182	C559	-1.4876296	-0.0265439	-0.7952792	0.2265450
61	1.2452	0.5386	-0.7657	A662	C175	1.9954496	0.9735682	-0.8296280	0.4163819
62	-0.8474	-1.8388	-0.9997	A377	C802	-1.5935443	-1.4685237	-0.8727753	0.4144484
63	-0.1779	-1.1912	-0.6058	A452	C655	-0.2597926	-1.1730025	-0.5212327	0.0615525
64	-1.8148	-1.3607	-0.9634	A165	C802	-1.5935443	-1.4685237	-0.8727753	0.1399013
65	1.5954	0.3825	-0.9332	A699	C175	1.9954496	0.9735682	-0.8296280	0.3648966
66	0.3358	-1.0062	-0.3433	A515	C655	-0.2597926	-1.1730025	-0.5212327	0.3134426
67	0.4931	1.4412	-0.8790	A530	C287	0.5468719	1.0211322	-0.4670886	0.2952504
68	-0.1928	1.4034	-0.8122	A427	C342	-0.8373696	1.1920791	-0.7640059	0.3013615
69	-0.7097	0.8380	-0.4320	A351	C342	-0.8373696	1.1920791	-0.7640059	0.2712515
70	0.2112	-1.0659	-0.4072	A497	C655	-0.2597926	-1.1730025	-0.5212327	0.2307092
71	-2.7841	-1.0335	0.2443	A18	C766	-2.7284759	-0.4976307	-0.3415241	0.3924392
72	2.5392	0.6095	-0.7914	A817	C175	1.9954496	0.9735682	-0.8296280	0.3153489
73	0.8731	0.5892	-0.3220	A574	C287	0.5468719	1.0211322	-0.4670886	0.3010830
74	-0.3964	2.8367	-0.5030	A353	C123	-0.9422671	2.4806302	-0.5791599	0.3260323
75	-0.6241	-0.8163	0.2330	A386	C536	-1.0323493	-0.1417128	0.3010375	0.3836246
76	-0.8246	0.7208	0.4259	A331	C350	-0.5144181	1.0433207	0.4973778	0.2347268
77	-0.6428	-2.8511	-0.3856	A384	C881	-0.5693053	-2.7024202	-0.2819962	0.1085927
78	0.0723	2.8472	0.5298	A440	C100	-0.0270481	2.4238631	0.7389638	0.2439496
79	0.9119	0.5508	0.3555	A590	C397	1.0336915	0.2140921	0.0921008	0.2406329
80	0.7259	1.9307	0.9980	A572	C228	0.8994003	1.2236527	0.8271905	0.3504523
81	0.6946	1.0625	-0.6828	A546	C287	0.5468719	1.0211322	-0.4670886	0.1349358
82	-0.0717	-1.0904	-0.4207	A465	C655	-0.2597926	-1.1730025	-0.5212327	0.1237426
83	0.7083	-0.8675	-0.4747	A583	C556	0.6025305	-0.9291853	0.3583787	0.3335112
84	0.3235	-1.4419	0.8528	A539	C710	-0.4532110	-1.5200102	0.8113151	0.2987687
85	0.7369	2.8276	-0.3870	A569	C81	0.5783356	2.3154644	-0.7661384	0.3499461
86	-1.1345	0.0258	0.5014	A265	C536	-1.0323493	-0.1417128	0.3010375	0.1566754
87	0.6531	-0.7803	0.1866	A565	C556	0.6025305	-0.9291853	0.3583787	0.1237445
88	-0.5404	-0.8417	0.0229	A393	C655	-0.2597926	-1.1730025	-0.5212327	0.3853475
89	-1.1039	-1.5202	0.9926	A253	C710	-0.4532110	-1.5200102	0.8113151	0.2773879
90	1.0478	-0.2977	-0.4130	A625	C397	1.0336915	0.2140921	0.0921008	0.3436671
91	2.5181	1.4823	0.3873	A857	B2	2.4722545	1.6685091	0.1332182	0.1620455
92	0.6162	1.5149	-0.9312	A582	C81	0.5783356	2.3154644	-0.7661384	0.3344968
93	-0.4433	-1.1454	0.6358	A391	C710	-0.4532110	-1.5200102	0.8113151	0.1866788
94	1.3759	-0.7827	-0.9089	A713	C508	1.3298237	-0.7586967	-0.8086783	0.0567671
95	-0.1227	2.1938	0.9804	A444	C100	-0.0270481	2.4238631	0.7389638	0.1890504
96	-1.0680	0.0576	0.3665	A294	C536	-1.0323493	-0.1417128	0.3010375	0.1001420
97	1.4713	-1.2646	-0.9982	A738	C508	1.3298237	-0.7586967	-0.8086783	0.2789671
98	1.3807	-1.1771	-0.9826	A727	C508	1.3298237	-0.7586967	-0.8086783	0.2144004
99	-2.2003	1.7828	0.5549	A58	C224	-1.4293520	1.9746821	0.7526839	0.3868713
100	0.7943	-2.1370	0.9601	A680	C763	0.7912866	-2.2489217	0.7766609	0.0994581
101	1.4817	-1.5140	0.9930	A759	C459	1.7910516	-0.5739146	0.9028013	0.4465452
102	0.1225	-1.6881	-0.9516	A521	C655	-0.2597926	-1.1730025	-0.5212327	0.4425858
103	-1.2855	0.6185	-0.8192	A239	C559	-1.4876296	-0.0265439	-0.7952792	0.2903648
104	2.1031	-1.7084	0.7047	A867	C676	2.1950559	-1.7495404	0.0972307	0.2468552
105	1.0015	-0.0265	0.0615	A605	C397	1.0336915	0.2140921	0.0921008	0.1011281
106	1.9526	-1.4518	-0.9013	A834	C508	1.3298237	-0.7586967	-0.8086783	0.4695004
107	-2.5264	-0.4163	0.8282	A74	C728	-1.9816416	-0.8223302	0.8717976	0.3314621
108	0.9461	0.3276	0.0501	A591	C397	1.0336915	0.2140921	0.0921008	0.0810334
109	1.0186	-2.7007	-0.4628	A787	C776	0.8378659	-2.2297098	-0.7821201	0.3236814
110	0.6176	-1.1895	-0.7515	A587	C655	-0.2597926	-1.1730025	-0.5212327	0.3747191
111	-0.9425	-1.2818	-0.9125	A318	C802	-1.5935443	-1.4685237	-0.8727753	0.2924976
112	-0.8158	-1.2295	0.8514	A348	C710	-0.4532110	-1.5200102	0.8113151	0.2310613
113	-1.1540	1.2490	0.9541	A225	C224	-1.4293520	1.9746821	0.7526839	0.4008167
114	1.6739	-1.9265	0.8337	A798	C763	0.7912866	-2.2489217	0.7766609	0.4206914
115	1.0136	0.0642	-0.1760	A615	C397	1.0336915	0.2140921	0.0921008	0.1460281
116	2.3592	-0.3831	-0.9208	A819	C368	2.7225869	-0.3304495	-0.3889044	0.3159777
117	2.6676	-0.7362	0.6413	A886	C459	1.7910516	-0.5739146	0.9028013	0.4334450
118	1.3552	-1.2410	0.9867	A712	C459	1.7910516	-0.5739146	0.9028013	0.3956119
119	-2.3549	-1.7335	-0.3820	A79	C802	-1.5935443	-1.4685237	-0.8727753	0.5057024
120	-0.8808	2.7421	0.4748	A197	C123	-0.9422671	2.4806302	-0.5791599	0.4589656
121	1.4617	0.2628	0.8573	A685	C459	1.7910516	-0.5739146	0.9028013	0.4038558
122	1.9630	-1.9542	-0.6382	A843	C676	2.1950559	-1.7495404	0.0972307	0.3907154
123	0.7405	-1.4611	0.9322	A658	C763	0.7912866	-2.2489217	0.7766609	0.3313825
124	1.7961	1.8374	-0.8220	A764	C175	1.9954496	0.9735682	-0.8296280	0.3569364
125	-0.9862	0.4363	0.3883	A299	C536	-1.0323493	-0.1417128	0.3010375	0.2371415
126	1.9863	-0.1731	-1.0000	A791	C175	1.9954496	0.9735682	-0.8296280	0.4420633
127	0.4657	1.3142	-0.7957	A545	C287	0.5468719	1.0211322	-0.4670886	0.2342837
128	-0.9237	-1.0104	0.7758	A347	C710	-0.4532110	-1.5200102	0.8113151	0.3385381
129	-0.8115	-0.5881	-0.0663	A356	C536	-1.0323493	-0.1417128	0.3010375	0.3448580
130	-1.0989	1.7631	0.9970	A233	C224	-1.4293520	1.9746821	0.7526839	0.2621167
131	-0.3163	-1.5032	0.8859	A399	C710	-0.4532110	-1.5200102	0.8113151	0.0761020
132	-0.9674	-2.1010	-0.9497	A291	C802	-1.5935443	-1.4685237	-0.8727753	0.4451818
133	-0.3055	-2.9567	-0.2330	A471	C881	-0.5693053	-2.7024202	-0.2819962	0.1890271
134	1.7911	-2.4055	0.0424	A863	B3	1.7531600	-2.4276200	-0.0842200	0.0622267
135	0.1502	1.2472	0.6684	A463	C228	0.8994003	1.2236527	0.8271905	0.3105127
136	2.5995	0.0603	0.7998	A856	C160	2.3972612	0.8131370	0.6512993	0.3678588
137	1.3080	2.3847	0.6942	A716	C29	1.5896815	2.2890353	0.3101313	0.2538050
138	-2.0506	-1.7103	0.7422	A94	C873	-1.6544946	-2.1236132	0.5230898	0.3428429
139	-2.2046	1.7247	0.6012	A58	C224	-1.4293520	1.9746821	0.7526839	0.3922380
140	1.9431	-1.6426	-0.8389	A834	C676	2.1950559	-1.7495404	0.0972307	0.4316757
141	2.4125	-1.7647	0.1478	A897	C676	2.1950559	-1.7495404	0.0972307	0.0943910
142	0.9843	0.5758	0.5109	A590	C397	1.0336915	0.2140921	0.0921008	0.2766329
143	1.0159	-1.7361	0.9999	A705	C763	0.7912866	-2.2489217	0.7766609	0.3202247
144	-2.0010	-1.1402	-0.9530	A145	C802	-1.5935443	-1.4685237	-0.8727753	0.2720013
145	-2.6670	0.2138	-0.7373	A61	C766	-2.7284759	-0.4976307	-0.3415241	0.3895608
146	0.9120	-2.6983	-0.5296	A733	C776	0.8378659	-2.2297098	-0.7821201	0.2650814
147	-0.8105	-0.8370	0.5505	A339	C536	-1.0323493	-0.1417128	0.3010375	0.3888663
148	-1.1088	0.5431	-0.6437	A286	C342	-0.8373696	1.1920791	-0.7640059	0.3469051
149	-1.5342	1.5302	0.9860	A158	C224	-1.4293520	1.9746821	0.7526839	0.2608821
150	-0.6017	-0.8157	0.1641	A397	C536	-1.0323493	-0.1417128	0.3010375	0.4138580
151	2.7037	0.8258	-0.5622	A841	C175	1.9954496	0.9735682	-0.8296280	0.3744822
152	-0.2688	2.8450	-0.5142	A411	C123	-0.9422671	2.4806302	-0.5791599	0.3675989
153	2.3089	-1.8491	0.2865	A897	C676	2.1950559	-1.7495404	0.0972307	0.1342243
154	-0.5111	1.7135	-0.9773	A382	C342	-0.8373696	1.1920791	-0.7640059	0.3536615
155	1.6935	1.5562	-0.9540	A764	C175	1.9954496	0.9735682	-0.8296280	0.3363178
156	-1.5252	1.1671	-0.9968	A199	C342	-0.8373696	1.1920791	-0.7640059	0.3152012
157	0.8809	-1.7240	-0.9980	A707	C776	0.8378659	-2.2297098	-0.7821201	0.2548746
158	-2.0028	0.6976	0.9927	A138	C491	-2.1349643	0.6623576	0.8377438	0.1074543
159	-2.0008	0.7543	-0.9904	A148	C559	-1.4876296	-0.0265439	-0.7952792	0.4963783
160	-2.1050	2.0812	0.2793	A32	C224	-1.4293520	1.9746821	0.7526839	0.4185166
161	-1.4437	-0.1155	0.8340	A216	C536	-1.0323493	-0.1417128	0.3010375	0.3235087
162	-0.3028	-2.3989	0.9085	A417	C710	-0.4532110	-1.5200102	0.8113151	0.3754953
163	-0.5275	2.7514	-0.5980	A353	C123	-0.9422671	2.4806302	-0.5791599	0.2347923
164	-2.9708	0.1360	-0.2270	A2	C766	-2.7284759	-0.4976307	-0.3415241	0.3301596
165	-1.6253	-1.7889	0.9089	A194	C873	-1.6544946	-2.1236132	0.5230898	0.2499060
166	-0.9837	-1.4836	-0.9755	A306	C802	-1.5935443	-1.4685237	-0.8727753	0.2425484
167	0.3887	2.3230	0.9348	A488	C100	-0.0270481	2.4238631	0.7389638	0.2374825
168	-1.5514	-1.7777	-0.9332	A174	C802	-1.5935443	-1.4685237	-0.8727753	0.1372484
169	2.3619	-1.4712	-0.6225	A882	C676	2.1950559	-1.7495404	0.0972307	0.3883051
170	-1.6134	2.2074	0.6790	A103	C224	-1.4293520	1.9746821	0.7526839	0.1634833
171	-2.8701	0.6800	-0.3134	A25	C391	-2.3605439	1.3502882	-0.4417122	0.4360521
172	0.0281	-2.5211	0.8534	A517	C763	0.7912866	-2.2489217	0.7766609	0.3707013
173	1.1910	0.1690	0.6039	A638	C397	1.0336915	0.2140921	0.0921008	0.2380666
174	1.6529	0.3460	-0.9503	A732	C175	1.9954496	0.9735682	-0.8296280	0.3635966
175	2.2843	-1.5464	0.6517	A867	C676	2.1950559	-1.7495404	0.0972307	0.2822846
176	-0.9632	1.3705	-0.9457	A296	C342	-0.8373696	1.1920791	-0.7640059	0.1619818
177	-2.7227	-0.3113	0.6721	A45	C766	-2.7284759	-0.4976307	-0.3415241	0.4019102
178	-0.1444	-0.9903	0.0384	A448	C655	-0.2597926	-1.1730025	-0.5212327	0.2859092
179	-0.5450	-0.9203	-0.3665	A410	C655	-0.2597926	-1.1730025	-0.5212327	0.2308809
180	1.0290	-0.0197	-0.2397	A615	C397	1.0336915	0.2140921	0.0921008	0.1900948
181	-1.5460	-0.1751	0.8960	A216	C728	-1.9816416	-0.8223302	0.8717976	0.3690247
182	0.1672	1.1265	0.5083	A464	C350	-0.5144181	1.0433207	0.4973778	0.2585732
183	-0.9930	1.6979	0.9995	A233	C224	-1.4293520	1.9746821	0.7526839	0.3199834
184	-1.6401	1.8593	-0.8776	A120	C342	-0.8373696	1.1920791	-0.7640059	0.5278485
185	2.5630	0.7936	0.7304	A826	C160	2.3972612	0.8131370	0.6512993	0.0881255
186	0.9050	0.5243	-0.2994	A574	C397	1.0336915	0.2140921	0.0921008	0.2768001
187	-2.7567	0.9280	0.4174	A28	C491	-2.1349643	0.6623576	0.8377438	0.4359073
188	-0.1733	-1.7606	0.9730	A460	C710	-0.4532110	-1.5200102	0.8113151	0.2273953
189	1.9737	-0.3834	-0.9999	A761	C508	1.3298237	-0.7586967	-0.8086783	0.4034649
190	0.5154	1.3037	-0.8014	A545	C287	0.5468719	1.0211322	-0.4670886	0.2161170
191	1.3914	0.8905	0.9375	A671	C228	0.8994003	1.2236527	0.8271905	0.3118206
192	-1.8123	-2.3341	-0.2963	A109	C873	-1.6544946	-2.1236132	0.5230898	0.3958940
193	-0.8957	-0.4616	-0.1236	A330	C536	-1.0323493	-0.1417128	0.3010375	0.2937246
194	1.5544	1.0426	0.9917	A722	C228	0.8994003	1.2236527	0.8271905	0.3335206
195	2.0168	1.4473	0.8759	A777	C160	2.3972612	0.8131370	0.6512993	0.4130750
196	-2.0204	1.8397	-0.6808	A73	C391	-2.3605439	1.3502882	-0.4417122	0.3562145
197	-1.0481	0.2256	-0.3729	A300	C536	-1.0323493	-0.1417128	0.3010375	0.3523337
198	0.9191	-0.4546	0.2236	A595	C397	1.0336915	0.2140921	0.0921008	0.3049276
199	1.0440	2.3132	0.8430	A716	C29	1.5896815	2.2890353	0.3101313	0.3675716
200	-1.2530	-0.5141	0.7637	A259	C536	-1.0323493	-0.1417128	0.3010375	0.3519001
201	1.9651	-2.1665	-0.3802	A864	C676	2.1950559	-1.7495404	0.0972307	0.3747821
202	1.6332	1.3225	0.9948	A720	C228	0.8994003	1.2236527	0.8271905	0.3334188
203	-2.1669	0.3035	-0.9822	A107	C559	-1.4876296	-0.0265439	-0.7952792	0.3987450
204	1.1612	0.8264	0.8183	A631	C228	0.8994003	1.2236527	0.8271905	0.2226477
205	-0.4117	-2.9708	-0.0414	A471	C881	-0.5693053	-2.7024202	-0.2819962	0.2221938
206	0.2847	2.8304	0.5353	A499	C100	-0.0270481	2.4238631	0.7389638	0.3073163
207	1.0932	-2.2341	-0.8733	A740	C776	0.8378659	-2.2297098	-0.7821201	0.1169681
208	1.1414	1.7162	-0.9981	A665	C81	0.5783356	2.3154644	-0.7661384	0.4647635
209	0.6381	-1.2440	0.7986	A598	C556	0.6025305	-0.9291853	0.3583787	0.2635351
210	0.8282	0.5734	-0.1209	A561	C397	1.0336915	0.2140921	0.0921008	0.2592668
211	-2.2850	-0.2842	-0.9531	A101	C559	-1.4876296	-0.0265439	-0.7952792	0.4042824
212	2.2868	-0.8456	-0.8989	A832	C508	1.3298237	-0.7586967	-0.8086783	0.3780338
213	2.7590	-1.1072	0.2315	A892	C676	2.1950559	-1.7495404	0.0972307	0.4468512
214	-1.5119	-2.5762	-0.1604	A131	C881	-0.5693053	-2.7024202	-0.2819962	0.3968037
215	-1.6752	1.8646	-0.8622	A120	C342	-0.8373696	1.1920791	-0.7640059	0.5361818
216	0.1432	1.6464	0.9377	A439	C100	-0.0270481	2.4238631	0.7389638	0.3821491
217	-2.9970	-0.1086	0.0457	A3	C766	-2.7284759	-0.4976307	-0.3415241	0.3482596
218	-0.8717	0.7523	0.5291	A331	C350	-0.5144181	1.0433207	0.4973778	0.2266749
219	-2.0936	0.9503	-0.9542	A119	C391	-2.3605439	1.3502882	-0.4417122	0.3931400
220	-1.0274	0.3241	-0.3856	A300	C536	-1.0323493	-0.1417128	0.3010375	0.3857999
221	1.2868	-1.7138	-0.9897	A714	C776	0.8378659	-2.2297098	-0.7821201	0.3908080
222	-0.6468	-0.8173	0.2876	A386	C536	-1.0323493	-0.1417128	0.3010375	0.3581913
223	0.6136	-2.2540	-0.9419	A667	C776	0.8378659	-2.2297098	-0.7821201	0.1361120
224	-2.0174	-2.2184	0.0542	A78	B6	-2.0145600	-2.2180200	-0.0545600	0.0373267
225	1.0539	-0.1411	-0.3502	A629	C397	1.0336915	0.2140921	0.0921008	0.2725671
226	0.8538	0.8230	0.5807	A563	C228	0.8994003	1.2236527	0.8271905	0.2309145
227	0.0124	1.5859	0.9102	A439	C100	-0.0270481	2.4238631	0.7389638	0.3495491
228	-0.9019	-0.8787	-0.6718	A313	C655	-0.2597926	-1.1730025	-0.5212327	0.3623258
229	-2.3119	-1.8911	0.1617	A52	B7	-2.3318600	-1.8725200	0.1143200	0.0286400
230	0.8256	-0.7831	-0.5067	A583	C508	1.3298237	-0.7586967	-0.8086783	0.2768685
231	-0.2416	1.9671	-0.9998	A418	C81	0.5783356	2.3154644	-0.7661384	0.4673205
232	1.2016	-1.2229	-0.9583	A693	C508	1.3298237	-0.7586967	-0.8086783	0.2473496
233	1.5170	2.5559	-0.2342	A788	C29	1.5896815	2.2890353	0.3101313	0.2946258
234	1.0998	2.2523	-0.8622	A674	C81	0.5783356	2.3154644	-0.7661384	0.2268968
235	-0.7354	-0.8398	-0.4681	A359	C655	-0.2597926	-1.1730025	-0.5212327	0.2873142
236	0.2757	-1.2167	0.6587	A504	C556	0.6025305	-0.9291853	0.3583787	0.3048888
237	-0.4936	-0.9218	-0.2986	A410	C655	-0.2597926	-1.1730025	-0.5212327	0.2358809
238	-0.9966	-0.2836	-0.2665	A312	C536	-1.0323493	-0.1417128	0.3010375	0.2483913
239	1.6170	-2.1425	-0.7293	A807	C776	0.8378659	-2.2297098	-0.7821201	0.3063880
240	0.0324	1.4142	-0.8107	A453	C342	-0.8373696	1.1920791	-0.7640059	0.3795282
241	2.4025	0.6102	-0.8780	A817	C175	1.9954496	0.9735682	-0.8296280	0.2729302
242	2.0478	0.0130	0.9989	A776	C459	1.7910516	-0.5739146	0.9028013	0.3132539
243	-0.3598	-2.5467	0.8203	A417	C710	-0.4532110	-1.5200102	0.8113151	0.3763619
244	1.1224	0.1561	0.4986	A624	C397	1.0336915	0.2140921	0.0921008	0.1843999
245	-0.9526	1.9024	0.9918	A254	C224	-1.4293520	1.9746821	0.7526839	0.2627167
246	-2.7771	-0.6502	0.5232	A17	C766	-2.7284759	-0.4976307	-0.3415241	0.3553058
247	2.4954	-0.1501	-0.8661	A840	C368	2.7225869	-0.3304495	-0.3889044	0.2949107
248	2.6805	0.2448	0.7222	A856	C160	2.3972612	0.8131370	0.6512993	0.3074922
249	-0.6946	0.8261	-0.3903	A375	C342	-0.8373696	1.1920791	-0.7640059	0.2941515
250	1.6103	1.3630	-0.9940	A725	C175	1.9954496	0.9735682	-0.8296280	0.3129845
251	-2.4856	-1.1832	0.6582	A69	C728	-1.9816416	-0.8223302	0.8717976	0.3594753
252	0.8406	2.5755	-0.7050	A618	C81	0.5783356	2.3154644	-0.7661384	0.1944795
253	0.9517	0.5432	0.4271	A590	C397	1.0336915	0.2140921	0.0921008	0.2486995
254	-0.7519	-0.6620	0.0599	A350	C536	-1.0323493	-0.1417128	0.3010375	0.3472913
255	-0.3917	-1.1634	0.6351	A428	C710	-0.4532110	-1.5200102	0.8113151	0.1981121
256	-1.7665	1.8294	-0.8397	A120	C391	-2.3605439	1.3502882	-0.4417122	0.4903812
257	-1.1453	-0.4333	-0.6314	A267	C559	-1.4876296	-0.0265439	-0.7952792	0.3043217
258	-0.7213	-0.6933	-0.0318	A380	C536	-1.0323493	-0.1417128	0.3010375	0.3984913
259	-0.8928	-1.3192	0.9134	A298	C710	-0.4532110	-1.5200102	0.8113151	0.2474947
260	-1.2444	2.3160	0.7773	A135	C224	-1.4293520	1.9746821	0.7526839	0.1836287
261	-0.4782	2.4709	-0.8561	A373	C123	-0.9422671	2.4806302	-0.5791599	0.2502458
262	-2.9793	0.3452	-0.0386	A2	C766	-2.7284759	-0.4976307	-0.3415241	0.4655263
263	-2.4541	0.0480	0.8907	A67	C491	-2.1349643	0.6623576	0.8377438	0.3288165
264	0.0796	-2.9885	0.1440	A666	C881	-0.5693053	-2.7024202	-0.2819962	0.4536604
265	-1.7892	2.2056	0.5426	A68	C224	-1.4293520	1.9746821	0.7526839	0.2669499
266	1.1087	-2.5569	-0.6171	A772	C776	0.8378659	-2.2297098	-0.7821201	0.2543481
267	0.6156	1.2375	-0.7863	A545	C287	0.5468719	1.0211322	-0.4670886	0.2014358
268	1.5634	-2.3616	0.5544	A820	C763	0.7912866	-2.2489217	0.7766609	0.3690175
269	-2.3775	1.6492	-0.4491	A26	C391	-2.3605439	1.3502882	-0.4417122	0.1077519
270	-0.2225	2.4739	-0.8751	A400	C123	-0.9422671	2.4806302	-0.5791599	0.3408124
271	1.3465	-0.2928	-0.7830	A679	C508	1.3298237	-0.7586967	-0.8086783	0.1694171
272	0.7115	0.8419	0.4405	A552	C228	0.8994003	1.2236527	0.8271905	0.3187812
273	-0.1743	-1.3260	0.7490	A470	C710	-0.4532110	-1.5200102	0.8113151	0.1784121
274	-0.0313	1.1459	0.5209	A433	C350	-0.5144181	1.0433207	0.4973778	0.2030732
275	1.4445	0.1989	-0.8404	A678	C508	1.3298237	-0.7586967	-0.8086783	0.3679982
276	-1.1680	-2.7626	0.0366	A224	C881	-0.5693053	-2.7024202	-0.2819962	0.3258235
277	-2.7299	0.1986	-0.6758	A49	C766	-2.7284759	-0.4976307	-0.3415241	0.3439769
278	-0.3458	-1.0756	-0.4927	A437	C655	-0.2597926	-1.1730025	-0.5212327	0.0706475
279	-1.9696	-2.0643	-0.5217	A116	C802	-1.5935443	-1.4685237	-0.8727753	0.4409691
280	-1.1870	-2.3036	-0.8064	A232	C802	-1.5935443	-1.4685237	-0.8727753	0.4359987
281	-0.8834	-2.6109	-0.6542	A270	C881	-0.5693053	-2.7024202	-0.2819962	0.2592729
282	-1.3442	0.8076	0.9019	A218	C491	-2.1349643	0.6623576	0.8377438	0.3333876
283	0.7163	2.6764	0.6373	A589	C100	-0.0270481	2.4238631	0.7389638	0.3658496
284	1.0152	1.4673	0.9765	A635	C228	0.8994003	1.2236527	0.8271905	0.1695855
285	-0.4213	-1.6038	-0.9398	A436	C655	-0.2597926	-1.1730025	-0.5212327	0.3369574
286	0.6093	-1.5148	0.9301	A598	C763	0.7912866	-2.2489217	0.7766609	0.3565158
287	-1.4382	-2.5829	0.2925	A157	C873	-1.6544946	-2.1236132	0.5230898	0.3020571
288	1.0546	-2.1339	-0.9249	A740	C776	0.8378659	-2.2297098	-0.7821201	0.1517746
289	-0.8928	-0.5288	-0.2718	A335	C536	-1.0323493	-0.1417128	0.3010375	0.3664913
290	-2.1225	-1.1611	-0.9078	A123	C802	-1.5935443	-1.4685237	-0.8727753	0.2904680
291	-0.6258	0.8040	0.1935	A379	C350	-0.5144181	1.0433207	0.4973778	0.2181935
292	-0.5799	0.9510	0.4633	A378	C350	-0.5144181	1.0433207	0.4973778	0.0639601
293	-0.9771	0.2480	-0.1271	A315	C536	-1.0323493	-0.1417128	0.3010375	0.2910332
294	-0.0433	1.1488	-0.5261	A432	C287	0.5468719	1.0211322	-0.4670886	0.2589504
295	-0.3417	-0.9614	-0.2005	A410	C655	-0.2597926	-1.1730025	-0.5212327	0.2047475
296	-1.3232	-1.5402	-0.9995	A243	C802	-1.5935443	-1.4685237	-0.8727753	0.1562484
297	1.7424	0.0223	-0.9663	A749	C175	1.9954496	0.9735682	-0.8296280	0.4469966
298	1.5469	2.4743	-0.3963	A782	C29	1.5896815	2.2890353	0.3101313	0.3114925
299	1.1774	0.0150	-0.5687	A641	C397	1.0336915	0.2140921	0.0921008	0.3345338
300	0.9640	0.2801	0.0878	A591	C397	1.0336915	0.2140921	0.0921008	0.0466668
301	1.0847	-2.5510	0.6355	A775	C763	0.7912866	-2.2489217	0.7766609	0.2455508
302	-1.0336	-0.2916	0.3773	A297	C536	-1.0323493	-0.1417128	0.3010375	0.0758001
303	-1.0885	2.0055	-0.9595	A238	C123	-0.9422671	2.4806302	-0.5791599	0.3339011
304	0.5061	1.5763	-0.9388	A530	C81	0.5783356	2.3154644	-0.7661384	0.3280205
305	-1.6592	-0.9932	0.9978	A166	C728	-1.9816416	-0.8223302	0.8717976	0.2064379
306	-0.3730	2.2686	0.9542	A363	C100	-0.0270481	2.4238631	0.7389638	0.2388170
307	-0.7274	-0.6915	0.0855	A362	C536	-1.0323493	-0.1417128	0.3010375	0.3567580
308	-1.7370	1.0884	0.9988	A155	C491	-2.1349643	0.6623576	0.8377438	0.3283543
309	1.5596	0.0911	-0.8991	A708	C508	1.3298237	-0.7586967	-0.8086783	0.3899982
310	-1.0926	0.9278	-0.8240	A282	C342	-0.8373696	1.1920791	-0.7640059	0.1931679
311	1.0063	-0.2067	-0.2321	A612	C397	1.0336915	0.2140921	0.0921008	0.2574615
312	2.7954	1.0744	0.1024	A861	C160	2.3972612	0.8131370	0.6512993	0.4027670
313	0.0849	-1.7737	0.9745	A527	C710	-0.4532110	-1.5200102	0.8113151	0.3183286
314	0.6582	-0.8703	0.4171	A584	C556	0.6025305	-0.9291853	0.3583787	0.0577587
315	1.4296	0.3573	-0.8502	A699	C175	1.9954496	0.9735682	-0.8296280	0.4008966
316	2.8610	-0.4488	0.4441	A886	C368	2.7225869	-0.3304495	-0.3889044	0.3632560
317	-2.3910	-0.2676	0.9139	A74	C728	-1.9816416	-0.8223302	0.8717976	0.3353970
318	-0.4076	2.4035	-0.8991	A373	C123	-0.9422671	2.4806302	-0.5791599	0.3105791
319	-2.1250	-2.0712	-0.2532	A78	B9	-2.1029000	-2.1281333	-0.1161000	0.0720444
320	-1.2351	0.7357	-0.8269	A239	C342	-0.8373696	1.1920791	-0.7640059	0.3056679
321	1.4941	-0.1584	-0.8675	A724	C508	1.3298237	-0.7586967	-0.8086783	0.2744649
322	-2.0356	-0.7430	-0.9860	A151	C802	-1.5935443	-1.4685237	-0.8727753	0.4269347
323	0.4255	-0.9368	0.2386	A551	C556	0.6025305	-0.9291853	0.3583787	0.1014747
324	-1.9315	1.1602	0.9674	A110	C491	-2.1349643	0.6623576	0.8377438	0.2769876
325	-2.4558	-0.8313	-0.8055	A95	C766	-2.7284759	-0.4976307	-0.3415241	0.3567737
326	0.0204	-1.0267	-0.2302	A481	C655	-0.2597926	-1.1730025	-0.5212327	0.2391759
327	-0.8167	0.6633	-0.3188	A345	C342	-0.8373696	1.1920791	-0.7640059	0.3315515
328	-0.0444	1.3000	-0.7149	A453	C342	-0.8373696	1.1920791	-0.7640059	0.3166655
329	-1.0868	-1.9677	0.9688	A269	C873	-1.6544946	-2.1236132	0.5230898	0.3897727
330	-0.2371	-1.1793	0.6038	A428	C710	-0.4532110	-1.5200102	0.8113151	0.2547788
331	1.9114	1.2923	0.9516	A777	C228	0.8994003	1.2236527	0.8271905	0.4016855
332	2.8893	-0.0213	0.4571	A884	C368	2.7225869	-0.3304495	-0.3889044	0.4406223
333	2.0531	-0.1496	0.9983	A778	C459	1.7910516	-0.5739146	0.9028013	0.2606206
334	2.4880	-0.8520	0.7768	A844	C459	1.7910516	-0.5739146	0.9028013	0.3670117
335	0.0912	-1.4476	-0.8355	A494	C655	-0.2597926	-1.1730025	-0.5212327	0.3132858
336	-0.4304	2.9230	-0.2982	A262	C123	-0.9422671	2.4806302	-0.5791599	0.4117323
337	-2.0945	-0.0008	0.9955	A122	C491	-2.1349643	0.6623576	0.8377438	0.2871260
338	2.1400	1.9871	0.3912	A835	C29	1.5896815	2.2890353	0.3101313	0.3111075
339	0.8738	-1.1722	0.8430	A654	C556	0.6025305	-0.9291853	0.3583787	0.3329685
340	0.8131	-0.5880	-0.0823	A573	C556	0.6025305	-0.9291853	0.3583787	0.3308112
341	-1.0363	2.6143	0.5834	A160	C224	-1.4293520	1.9746821	0.7526839	0.4006513
342	-1.8418	1.2375	-0.9758	A129	C391	-2.3605439	1.3502882	-0.4417122	0.3885400
343	-1.5560	2.4888	0.3541	A96	C224	-1.4293520	1.9746821	0.7526839	0.3464499
344	0.7963	0.6052	0.0197	A561	C397	1.0336915	0.2140921	0.0921008	0.2336334
345	1.4120	-2.5998	0.2850	A813	C763	0.7912866	-2.2489217	0.7766609	0.4877508
346	2.9746	-0.3190	0.1292	A891	C368	2.7225869	-0.3304495	-0.3889044	0.2605223
347	0.3221	-1.4040	-0.8288	A540	C655	-0.2597926	-1.1730025	-0.5212327	0.3734858
348	1.8709	0.5720	0.9990	A753	C160	2.3972612	0.8131370	0.6512993	0.3717330
349	0.7973	0.7526	0.4284	A567	C228	0.8994003	1.2236527	0.8271905	0.3239812
350	1.0028	2.7593	-0.3524	A687	C81	0.5783356	2.3154644	-0.7661384	0.4273461
351	-0.2160	2.0072	-0.9998	A418	C81	0.5783356	2.3154644	-0.7661384	0.4454205
352	0.8964	-2.5208	0.7375	A734	C763	0.7912866	-2.2489217	0.7766609	0.1387175
353	-1.9078	-0.0432	-0.9958	A171	C559	-1.4876296	-0.0265439	-0.7952792	0.2124491
354	-1.8749	0.4005	0.9966	A125	C491	-2.1349643	0.6623576	0.8377438	0.2269260
355	2.8941	0.7374	-0.1636	A874	C160	2.3972612	0.8131370	0.6512993	0.4624917
356	-1.3407	2.6730	0.1381	A137	C123	-0.9422671	2.4806302	-0.5791599	0.4360209
357	-2.1526	-1.9957	0.3537	A64	C873	-1.6544946	-2.1236132	0.5230898	0.2651361
358	0.5472	-0.9365	-0.4026	A544	C556	0.6025305	-0.9291853	0.3583787	0.2745413
359	0.9346	0.4142	0.2100	A575	C397	1.0336915	0.2140921	0.0921008	0.1390329
360	-0.8375	-2.8615	-0.1912	A245	C881	-0.5693053	-2.7024202	-0.2819962	0.1726902
361	0.9915	0.1417	0.0561	A605	C397	1.0336915	0.2140921	0.0921008	0.0501948
362	-2.1207	1.8959	0.5354	A58	C224	-1.4293520	1.9746821	0.7526839	0.3291380
363	-2.7875	0.8928	0.3752	A28	C491	-2.1349643	0.6623576	0.8377438	0.4485073
364	2.3448	-0.2259	-0.9346	A815	C368	2.7225869	-0.3304495	-0.3889044	0.3426773
365	-0.3161	-0.9520	-0.0783	A413	C655	-0.2597926	-1.1730025	-0.5212327	0.2400809
366	0.5056	-1.6712	0.9672	A593	C763	0.7912866	-2.2489217	0.7766609	0.3513158
367	2.5225	-1.1151	-0.6522	A854	C368	2.7225869	-0.3304495	-0.3889044	0.4160110
368	0.9420	0.5021	-0.3610	A574	C397	1.0336915	0.2140921	0.0921008	0.2776001
369	-0.0337	1.0108	0.1506	A443	C350	-0.5144181	1.0433207	0.4973778	0.2866722
370	0.2211	-1.4546	0.8488	A539	C710	-0.4532110	-1.5200102	0.8113151	0.2590687
371	1.1492	2.6872	0.3856	A741	C29	1.5896815	2.2890353	0.3101313	0.3047050
372	-1.2287	0.9782	0.9031	A226	C350	-0.5144181	1.0433207	0.4973778	0.3950416
373	1.2111	0.7226	0.8076	A631	C228	0.8994003	1.2236527	0.8271905	0.2774477
374	-0.5065	-1.3311	0.8176	A420	C710	-0.4532110	-1.5200102	0.8113151	0.0828280
375	2.8026	-0.6051	-0.4980	A869	C368	2.7225869	-0.3304495	-0.3889044	0.1545864
376	-1.9062	1.6976	0.8335	A115	C224	-1.4293520	1.9746821	0.7526839	0.2782487
377	-0.2430	1.6462	-0.9419	A442	C342	-0.8373696	1.1920791	-0.7640059	0.4087949
378	-2.9173	0.0762	0.3960	A14	C766	-2.7284759	-0.4976307	-0.3415241	0.5000596
379	-1.3877	0.5988	0.8725	A207	C491	-2.1349643	0.6623576	0.8377438	0.2818594
380	2.3793	0.7312	-0.8722	A817	C175	1.9954496	0.9735682	-0.8296280	0.2229302
381	-1.7840	0.9500	0.9998	A155	C491	-2.1349643	0.6623576	0.8377438	0.2668876
382	-0.6415	-2.6880	0.6459	A340	C881	-0.5693053	-2.7024202	-0.2819962	0.3381704
383	2.7061	0.4466	-0.6696	A841	C368	2.7225869	-0.3304495	-0.3889044	0.3580773
384	0.2882	1.1475	-0.5769	A501	C287	0.5468719	1.0211322	-0.4670886	0.1649504
385	-1.3451	-0.2113	-0.7697	A236	C559	-1.4876296	-0.0265439	-0.7952792	0.1176217
386	2.4710	-1.6877	0.1235	A900	C676	2.1950559	-1.7495404	0.0972307	0.1213512
387	2.1174	-0.6165	0.9787	A814	C459	1.7910516	-0.5739146	0.9028013	0.1482775
388	0.6487	-1.3299	0.8540	A598	C556	0.6025305	-0.9291853	0.3583787	0.3141685
389	-1.7043	-1.2978	0.9898	A172	C728	-1.9816416	-0.8223302	0.8717976	0.2902712
390	0.8384	-1.6579	0.9898	A656	C763	0.7912866	-2.2489217	0.7766609	0.2837581
391	1.4744	1.4139	0.9991	A720	C228	0.8994003	1.2236527	0.8271905	0.3123855
392	-0.3011	2.2148	-0.9720	A365	C81	0.5783356	2.3154644	-0.7661384	0.3953205
393	-1.4500	-0.0603	0.8360	A216	C536	-1.0323493	-0.1417128	0.3010375	0.3446754
394	0.9978	0.7111	-0.6323	A608	C287	0.5468719	1.0211322	-0.4670886	0.3087239
395	0.8008	2.8417	-0.3049	A689	C81	0.5783356	2.3154644	-0.7661384	0.4033128
396	-1.3226	-1.3485	0.9938	A229	C710	-0.4532110	-1.5200102	0.8113151	0.4077947
397	1.0562	1.7626	0.9985	A653	C228	0.8994003	1.2236527	0.8271905	0.2890188
398	-0.0692	1.0299	-0.2519	A451	C287	0.5468719	1.0211322	-0.4670886	0.2800095
399	0.2158	-1.9865	-1.0000	A520	C776	0.8378659	-2.2297098	-0.7821201	0.3610519
400	0.1887	-2.7517	-0.6521	A602	C881	-0.5693053	-2.7024202	-0.2819962	0.3924630
401	-2.1051	1.4023	0.8484	A110	C491	-2.1349643	0.6623576	0.8377438	0.2601543
402	-2.1389	-1.0245	0.9284	A98	C728	-1.9816416	-0.8223302	0.8717976	0.1386769
403	2.0265	1.5842	0.8201	A800	C160	2.3972612	0.8131370	0.6512993	0.4368750
404	-1.7133	-1.0398	-1.0000	A191	C802	-1.5935443	-1.4685237	-0.8727753	0.2252347
405	1.6418	2.0738	0.7642	A771	C29	1.5896815	2.2890353	0.3101313	0.2404742
406	0.5817	-0.8307	-0.1675	A560	C556	0.6025305	-0.9291853	0.3583787	0.2150649
407	-0.8107	1.3767	-0.9155	A296	C342	-0.8373696	1.1920791	-0.7640059	0.1209282
408	-0.8800	-0.7620	-0.5488	A359	C655	-0.2597926	-1.1730025	-0.5212327	0.3529258
409	-0.7606	-1.3396	-0.8882	A355	C802	-1.5935443	-1.4685237	-0.8727753	0.3257642
410	1.0168	0.3198	0.3570	A603	C397	1.0336915	0.2140921	0.0921008	0.1291662
411	-1.1287	-0.1060	-0.4995	A292	C559	-1.4876296	-0.0265439	-0.7952792	0.2447217
412	-1.9390	-0.7463	0.9970	A132	C728	-1.9816416	-0.8223302	0.8717976	0.0812914
413	2.3466	-0.5322	-0.9138	A819	C368	2.7225869	-0.3304495	-0.3889044	0.3675444
414	-0.2501	2.2383	0.9677	A363	C100	-0.0270481	2.4238631	0.7389638	0.2124504
415	-2.0594	0.4535	-0.9941	A148	C559	-1.4876296	-0.0265439	-0.7952792	0.4168783
416	0.8344	0.8220	0.5596	A563	C228	0.8994003	1.2236527	0.8271905	0.2447479
417	-0.7653	-0.6875	-0.2381	A356	C655	-0.2597926	-1.1730025	-0.5212327	0.4247142
418	-1.1293	1.8977	-0.9781	A235	C123	-0.9422671	2.4806302	-0.5791599	0.3896344
419	0.3701	-1.1362	0.5932	A504	C556	0.6025305	-0.9291853	0.3583787	0.2247555
420	0.5168	-1.1083	-0.6294	A542	C655	-0.2597926	-1.1730025	-0.5212327	0.3164875
421	-2.5775	0.7645	0.7253	A47	C491	-2.1349643	0.6623576	0.8377438	0.2190406
422	-0.1064	1.5462	0.8930	A439	C100	-0.0270481	2.4238631	0.7389638	0.3703504
423	-0.5925	1.4520	0.9020	A372	C350	-0.5144181	1.0433207	0.4973778	0.2971278
424	0.5320	0.9134	-0.3331	A519	C287	0.5468719	1.0211322	-0.4670886	0.0855309
425	-1.4327	-0.9187	0.9546	A200	C728	-1.9816416	-0.8223302	0.8717976	0.2427046
426	0.9802	1.4862	-0.9756	A643	C287	0.5468719	1.0211322	-0.4670886	0.4689691
427	-1.9605	-2.0767	0.5171	A91	C873	-1.6544946	-2.1236132	0.5230898	0.1196361
428	1.0085	0.1280	0.1812	A606	C397	1.0336915	0.2140921	0.0921008	0.0667942
429	-2.6172	1.4664	-0.0030	A9	C391	-2.3605439	1.3502882	-0.4417122	0.2704934
430	-2.5414	0.4990	-0.8075	A66	C391	-2.3605439	1.3502882	-0.4417122	0.4659774
431	1.1876	-0.4913	-0.6993	A675	C508	1.3298237	-0.7586967	-0.8086783	0.1729996
432	2.1612	-0.8554	-0.9460	A797	C508	1.3298237	-0.7586967	-0.8086783	0.3551338
433	0.1799	-2.9704	-0.2186	A666	C881	-0.5693053	-2.7024202	-0.2819962	0.3601938
434	1.1917	2.7325	-0.1935	A743	C29	1.5896815	2.2890353	0.3101313	0.4483592
435	-0.2787	1.3582	-0.7897	A388	C342	-0.8373696	1.1920791	-0.7640059	0.2501615
436	2.0500	1.0832	-0.9479	A758	C175	1.9954496	0.9735682	-0.8296280	0.0941514
437	-2.9684	0.1644	0.2310	A1	C766	-2.7284759	-0.4976307	-0.3415241	0.4914929
438	-1.6952	-0.5127	-0.9734	A185	C559	-1.4876296	-0.0265439	-0.7952792	0.2906157
439	-2.1498	-1.8794	-0.5179	A79	C802	-1.5935443	-1.4685237	-0.8727753	0.4406691
440	0.3174	1.4492	0.8563	A495	C228	0.8994003	1.2236527	0.8271905	0.2788857
441	2.7101	1.2437	-0.1899	A859	C160	2.3972612	0.8131370	0.6512993	0.5282003
442	1.6833	-0.9743	0.9985	A762	C459	1.7910516	-0.5739146	0.9028013	0.2012786
443	2.9184	-0.6856	-0.0661	A894	C368	2.7225869	-0.3304495	-0.3889044	0.2912560
444	1.3020	1.5686	-0.9993	A726	C175	1.9954496	0.9735682	-0.8296280	0.4860511
445	0.6424	-1.2173	-0.7818	A587	C508	1.3298237	-0.7586967	-0.8086783	0.3909685
446	-1.3237	0.5259	-0.8177	A239	C559	-1.4876296	-0.0265439	-0.7952792	0.2462648
447	-0.2194	-0.9802	0.0939	A441	C655	-0.2597926	-1.1730025	-0.5212327	0.2827759
448	1.3488	1.6659	0.9897	A704	C228	0.8994003	1.2236527	0.8271905	0.3513855
449	1.2692	-2.4183	-0.6823	A789	C776	0.8378659	-2.2297098	-0.7821201	0.2399148
450	-0.8346	2.2020	-0.9349	A279	C123	-0.9422671	2.4806302	-0.5791599	0.2473458
451	-1.1868	0.7765	-0.8134	A282	C342	-0.8373696	1.1920791	-0.7640059	0.2714679
452	0.0428	-2.5943	-0.8040	A571	C776	0.8378659	-2.2297098	-0.7821201	0.3938453
453	-2.0255	-2.0060	-0.5255	A116	C802	-1.5935443	-1.4685237	-0.8727753	0.4389024
454	1.7969	-1.6302	-0.9046	A816	C508	1.3298237	-0.7586967	-0.8086783	0.4781671
455	1.0190	1.0203	0.8298	A570	C228	0.8994003	1.2236527	0.8271905	0.1085206
456	0.1414	-1.2314	-0.6494	A487	C655	-0.2597926	-1.1730025	-0.5212327	0.1959191
457	-0.5333	-1.9817	-0.9986	A407	C881	-0.5693053	-2.7024202	-0.2819962	0.4911098
458	2.4433	1.6454	0.3252	A857	B2	2.4722545	1.6685091	0.1332182	0.0813485
459	1.1208	-1.9335	-0.9720	A707	C776	0.8378659	-2.2297098	-0.7821201	0.2563413
460	0.2676	1.1419	-0.5619	A501	C287	0.5468719	1.0211322	-0.4670886	0.1649504
461	1.8180	1.9627	-0.7375	A799	C175	1.9954496	0.9735682	-0.8296280	0.4195698
462	-0.9480	-0.5567	-0.4346	A335	C536	-1.0323493	-0.1417128	0.3010375	0.4116580
463	-0.9217	-0.5256	0.3441	A334	C536	-1.0323493	-0.1417128	0.3010375	0.1791997
464	0.0343	-1.1282	-0.4909	A497	C655	-0.2597926	-1.1730025	-0.5212327	0.1230759
465	2.6116	-1.1737	-0.5048	A877	C368	2.7225869	-0.3304495	-0.3889044	0.3567110
466	-1.9437	1.9565	-0.6524	A73	C391	-2.3605439	1.3502882	-0.4417122	0.4112479
467	0.7329	-1.1259	0.7542	A594	C556	0.6025305	-0.9291853	0.3583787	0.2409685
468	-1.0725	0.7896	-0.7440	A282	C342	-0.8373696	1.1920791	-0.7640059	0.2192051
469	-1.1248	0.9846	0.8630	A278	C350	-0.5144181	1.0433207	0.4973778	0.3449082
470	1.1734	-2.7267	0.2490	A813	C763	0.7912866	-2.2489217	0.7766609	0.4625175
471	0.4047	-1.0164	0.4233	A541	C556	0.6025305	-0.9291853	0.3583787	0.1166555
472	-1.4131	1.0380	-0.9691	A199	C342	-0.8373696	1.1920791	-0.7640059	0.3116345
473	1.2340	-2.0356	-0.9248	A740	C776	0.8378659	-2.2297098	-0.7821201	0.2443080
474	-0.7880	1.0447	0.7225	A323	C350	-0.5144181	1.0433207	0.4973778	0.1666945
475	0.2689	1.5452	0.9021	A495	C228	0.8994003	1.2236527	0.8271905	0.3423190
476	1.1494	-2.3854	-0.7617	A789	C776	0.8378659	-2.2297098	-0.7821201	0.1625481
477	1.0532	0.0476	0.3249	A620	C397	1.0336915	0.2140921	0.0921008	0.1395999
478	1.7797	-0.4347	0.9858	A735	C459	1.7910516	-0.5739146	0.9028013	0.0778550
479	0.3976	-1.2644	-0.7382	A535	C655	-0.2597926	-1.1730025	-0.5212327	0.3219191
480	0.7758	1.4078	-0.9197	A582	C287	0.5468719	1.0211322	-0.4670886	0.3560691
481	0.4750	-0.8848	-0.0918	A525	C556	0.6025305	-0.9291853	0.3583787	0.2073649
482	-1.1316	-0.3979	-0.5994	A288	C559	-1.4876296	-0.0265439	-0.7952792	0.3077550
483	-0.2287	1.1996	0.6273	A433	C350	-0.5144181	1.0433207	0.4973778	0.1906399
484	0.8988	0.9472	0.7198	A570	C228	0.8994003	1.2236527	0.8271905	0.1281479
485	1.3688	-1.8841	-0.9444	A780	C776	0.8378659	-2.2297098	-0.7821201	0.3462746
486	-0.2079	2.2405	0.9682	A363	C100	-0.0270481	2.4238631	0.7389638	0.1978170
487	2.4626	0.5365	-0.8539	A817	C175	1.9954496	0.9735682	-0.8296280	0.3094969
488	-0.6909	1.2117	-0.7961	A360	C342	-0.8373696	1.1920791	-0.7640059	0.0660615
489	-1.0013	-1.9960	-0.9725	A291	C802	-1.5935443	-1.4685237	-0.8727753	0.4064818
490	0.6596	1.1779	-0.7600	A562	C287	0.5468719	1.0211322	-0.4670886	0.1874691
491	-1.3578	0.5043	0.8341	A217	C491	-2.1349643	0.6623576	0.8377438	0.3129552
492	1.6388	2.2732	0.5968	A769	C29	1.5896815	2.2890353	0.3101313	0.1172075
493	0.7733	2.2118	-0.9393	A597	C81	0.5783356	2.3154644	-0.7661384	0.1572635
494	-0.2781	-2.5395	-0.8321	A447	C881	-0.5693053	-2.7024202	-0.2819962	0.3347431
495	-0.3880	0.9466	-0.2136	A402	C350	-0.5144181	1.0433207	0.4973778	0.3113722
496	-2.6445	1.2990	-0.3232	A43	C391	-2.3605439	1.3502882	-0.4417122	0.1512521
497	-0.0195	1.2793	-0.6934	A453	C342	-0.8373696	1.1920791	-0.7640059	0.3252321
498	-0.2179	1.5730	0.9112	A439	C100	-0.0270481	2.4238631	0.7389638	0.4046504
499	0.6854	1.0025	0.6187	A570	C228	0.8994003	1.2236527	0.8271905	0.2145479
500	0.4717	0.9042	0.1985	A514	C287	0.5468719	1.0211322	-0.4670886	0.2858976
501	1.2102	0.4784	-0.7154	A642	C397	1.0336915	0.2140921	0.0921008	0.4161058
502	-1.0548	1.2403	0.9283	A257	C350	-0.5144181	1.0433207	0.4973778	0.3894278
503	-0.9595	0.9431	0.7560	A278	C350	-0.5144181	1.0433207	0.4973778	0.2679749
504	0.5117	-1.0433	0.5457	A541	C556	0.6025305	-0.9291853	0.3583787	0.1307555
505	1.9741	0.5152	0.9992	A753	C160	2.3972612	0.8131370	0.6512993	0.3563330
506	0.2108	1.3245	-0.7523	A485	C287	0.5468719	1.0211322	-0.4670886	0.3082170
507	1.5322	-0.9358	0.9788	A750	C459	1.7910516	-0.5739146	0.9028013	0.2322452
508	0.3468	2.8532	0.4856	A499	C100	-0.0270481	2.4238631	0.7389638	0.3521830
509	0.8304	2.7676	0.4570	A700	C29	1.5896815	2.2890353	0.3101313	0.4615716
510	-1.4682	-2.4804	-0.4706	A176	C881	-0.5693053	-2.7024202	-0.2819962	0.4365062
511	-1.2791	0.0104	-0.6931	A247	C559	-1.4876296	-0.0265439	-0.7952792	0.1158843
512	0.1458	-1.8220	0.9851	A527	C710	-0.4532110	-1.5200102	0.8113151	0.3582619
513	1.3429	-0.3901	-0.7988	A675	C508	1.3298237	-0.7586967	-0.8086783	0.1305171
514	1.1035	0.0252	-0.4435	A629	C397	1.0336915	0.2140921	0.0921008	0.2647671
515	0.0764	2.4792	-0.8771	A450	C81	0.5783356	2.3154644	-0.7661384	0.2588776
516	1.8877	-1.0124	-0.9899	A792	C508	1.3298237	-0.7586967	-0.8086783	0.3309338
517	-1.0740	0.0666	-0.3824	A289	C559	-1.4876296	-0.0265439	-0.7952792	0.3065509
518	0.1753	-1.5575	0.9015	A502	C710	-0.4532110	-1.5200102	0.8113151	0.2520619
519	2.9330	0.1938	0.3429	A875	C160	2.3972612	0.8131370	0.6512993	0.4878250
520	1.7361	0.5279	-0.9827	A728	C175	1.9954496	0.9735682	-0.8296280	0.2860299
521	-0.0129	1.0273	0.2324	A457	C350	-0.5144181	1.0433207	0.4973778	0.2608389
522	2.6622	-0.1817	0.7438	A856	C368	2.7225869	-0.3304495	-0.3889044	0.4472802
523	-1.9281	0.6172	-0.9997	A148	C559	-1.4876296	-0.0265439	-0.7952792	0.4295450
524	0.5923	1.7831	0.9926	A543	C228	0.8994003	1.2236527	0.8271905	0.3439857
525	-0.9136	1.1281	-0.8362	A319	C342	-0.8373696	1.1920791	-0.7640059	0.0708012
526	-1.2492	2.7204	0.1138	A137	C123	-0.9422671	2.4806302	-0.5791599	0.4132209
527	-1.1091	2.0731	0.9363	A178	C224	-1.4293520	1.9746821	0.7526839	0.2007620
528	1.7230	2.4524	0.0754	A801	C29	1.5896815	2.2890353	0.3101313	0.1771382
529	-1.7771	1.7372	-0.8744	A120	C391	-2.3605439	1.3502882	-0.4417122	0.4676812
530	0.7123	1.5895	0.9661	A559	C228	0.8994003	1.2236527	0.8271905	0.2306190
531	-0.6103	0.8713	0.3514	A378	C350	-0.5144181	1.0433207	0.4973778	0.1379601
532	2.5170	-1.6221	0.1059	A900	C676	2.1950559	-1.7495404	0.0972307	0.1526846
533	0.5525	-2.8305	0.4677	A731	C763	0.7912866	-2.2489217	0.7766609	0.3764419
534	-2.8660	0.7535	0.2682	A12	C491	-2.1349643	0.6623576	0.8377438	0.4639073
535	-0.7979	2.8468	-0.2917	A169	C123	-0.9422671	2.4806302	-0.5791599	0.2659989
536	0.8266	-1.5932	-0.9787	A636	C776	0.8378659	-2.2297098	-0.7821201	0.2814519
537	-1.0539	1.1783	-0.9079	A272	C342	-0.8373696	1.1920791	-0.7640059	0.1247345
538	1.7245	0.2221	0.9653	A721	C459	1.7910516	-0.5739146	0.9028013	0.3083550
539	-0.7585	-2.3500	0.8830	A325	C710	-0.4532110	-1.5200102	0.8113151	0.4023212
540	1.5434	2.3476	0.5871	A769	C29	1.5896815	2.2890353	0.3101313	0.1272716
541	-1.7761	1.8648	0.8180	A117	C224	-1.4293520	1.9746821	0.7526839	0.1739821
542	0.8785	1.4512	-0.9528	A582	C287	0.5468719	1.0211322	-0.4670886	0.4158024
543	-1.2792	0.5948	0.8079	A258	C491	-2.1349643	0.6623576	0.8377438	0.3177219
544	1.2886	2.5218	-0.5548	A729	C81	0.5783356	2.3154644	-0.7661384	0.3759795
545	0.6734	-2.4831	0.8197	A698	C763	0.7912866	-2.2489217	0.7766609	0.1317013
546	2.1016	2.0340	-0.3806	A822	C29	1.5896815	2.2890353	0.3101313	0.4858950
547	0.9008	1.8007	-0.9999	A665	C81	0.5783356	2.3154644	-0.7661384	0.3569968
548	0.4848	-2.4347	-0.8759	A673	C776	0.8378659	-2.2297098	-0.7821201	0.2172787
549	-1.1883	2.6027	-0.5083	A159	C123	-0.9422671	2.4806302	-0.5791599	0.1463209
550	-0.4082	-2.8493	0.4779	A429	C881	-0.5693053	-2.7024202	-0.2819962	0.3559604
551	2.4223	-1.6368	0.3837	A897	C676	2.1950559	-1.7495404	0.0972307	0.2088179
552	0.7464	2.8849	-0.1995	A689	C81	0.5783356	2.3154644	-0.7661384	0.4347128
553	-2.2954	-0.5187	-0.9355	A101	C766	-2.7284759	-0.4976307	-0.3415241	0.3493737
554	-1.0275	2.4689	0.7386	A214	C224	-1.4293520	1.9746821	0.7526839	0.3033846
555	-1.2070	-0.6017	-0.7588	A268	C559	-1.4876296	-0.0265439	-0.7952792	0.2974217
556	2.8756	0.5547	0.3710	A875	C160	2.3972612	0.8131370	0.6512993	0.3390250
557	-2.0490	2.0938	0.3687	A32	C224	-1.4293520	1.9746821	0.7526839	0.3742499
558	2.8666	0.8810	0.0472	A861	C160	2.3972612	0.8131370	0.6512993	0.3804337
559	2.0854	0.6661	-0.9819	A783	C175	1.9954496	0.9735682	-0.8296280	0.1832302
560	1.2441	-1.4327	-0.9947	A714	C508	1.3298237	-0.7586967	-0.8086783	0.3152496
561	2.1864	-1.0290	-0.9092	A821	C508	1.3298237	-0.7586967	-0.8086783	0.4091338
562	-0.0345	1.3933	0.7953	A421	C100	-0.0270481	2.4238631	0.7389638	0.3647837
563	1.0682	0.0069	0.3629	A620	C397	1.0336915	0.2140921	0.0921008	0.1708332
564	1.0021	-0.1784	-0.1878	A612	C397	1.0336915	0.2140921	0.0921008	0.2346615
565	1.0443	0.1582	-0.3306	A615	C397	1.0336915	0.2140921	0.0921008	0.1630671
566	-2.1897	-1.2537	-0.8522	A124	C802	-1.5935443	-1.4685237	-0.8727753	0.2771849
567	-2.3062	-1.0998	0.8318	A98	C728	-1.9816416	-0.8223302	0.8717976	0.2140086
568	0.7843	0.6440	-0.1714	A549	C287	0.5468719	1.0211322	-0.4670886	0.3034163
569	-2.1368	-0.3717	0.9856	A128	C728	-1.9816416	-0.8223302	0.8717976	0.2398637
570	-0.7365	1.2947	-0.8599	A360	C342	-0.8373696	1.1920791	-0.7640059	0.0997949
571	-0.8306	0.6273	-0.2830	A327	C342	-0.8373696	1.1920791	-0.7640059	0.3508515
572	0.8643	-0.5305	0.1675	A595	C556	0.6025305	-0.9291853	0.3583787	0.2837778
573	-1.5358	-1.7021	-0.9562	A209	C802	-1.5935443	-1.4685237	-0.8727753	0.1249151
574	1.6627	-0.6821	0.9792	A748	C459	1.7910516	-0.5739146	0.9028013	0.1043119
575	1.5036	0.9017	0.9691	A696	C228	0.8994003	1.2236527	0.8271905	0.3560206
576	-1.7199	-2.3959	-0.3144	A109	C873	-1.6544946	-2.1236132	0.5230898	0.3917273
577	-1.8413	-2.1474	-0.5597	A109	C802	-1.5935443	-1.4685237	-0.8727753	0.4132358
578	0.4249	-2.5856	-0.7844	A673	C776	0.8378659	-2.2297098	-0.7821201	0.2570453
579	1.8306	1.7774	0.8342	A770	C29	1.5896815	2.2890353	0.3101313	0.4255408
580	0.2499	-2.8312	0.5392	A617	C763	0.7912866	-2.2489217	0.7766609	0.4537086
581	1.8045	-0.4491	0.9901	A748	C459	1.7910516	-0.5739146	0.9028013	0.0751873
582	0.9368	-0.3697	-0.1194	A601	C397	1.0336915	0.2140921	0.0921008	0.2973948
583	0.0556	-2.6300	0.7761	A576	C763	0.7912866	-2.2489217	0.7766609	0.3724419
584	0.5579	-1.3443	0.8387	A598	C556	0.6025305	-0.9291853	0.3583787	0.3133555
585	-1.1061	0.0391	-0.4497	A289	C559	-1.4876296	-0.0265439	-0.7952792	0.2642509
586	0.9597	0.7357	-0.6122	A608	C287	0.5468719	1.0211322	-0.4670886	0.2811239
587	-1.6901	-1.1723	-0.9984	A191	C802	-1.5935443	-1.4685237	-0.8727753	0.1728013
588	0.9368	1.0523	-0.8066	A585	C287	0.5468719	1.0211322	-0.4670886	0.2535358
589	-2.3316	1.2498	-0.7639	A81	C391	-2.3605439	1.3502882	-0.4417122	0.1505400
590	-0.9890	1.0117	0.8109	A278	C350	-0.5144181	1.0433207	0.4973778	0.2732416
591	-2.0021	-2.1748	-0.2934	A109	C873	-1.6544946	-2.1236132	0.5230898	0.4050940
592	-0.1603	-1.0768	0.4116	A456	C556	0.6025305	-0.9291853	0.3583787	0.3212222
593	-0.9532	-0.7275	0.5987	A339	C536	-1.0323493	-0.1417128	0.3010375	0.3208663
594	-0.5129	0.8839	0.2085	A398	C350	-0.5144181	1.0433207	0.4973778	0.1499389
595	1.4614	0.0455	0.8430	A691	C459	1.7910516	-0.5739146	0.9028013	0.3362892
596	-0.9947	0.1520	0.1118	A310	C536	-1.0323493	-0.1417128	0.3010375	0.1735332
597	1.1992	0.6798	-0.7834	A646	C175	1.9954496	0.9735682	-0.8296280	0.3787486
598	2.0263	-0.5415	-0.9952	A797	C508	1.3298237	-0.7586967	-0.8086783	0.3667315
599	0.5356	-1.6339	0.9598	A593	C763	0.7912866	-2.2489217	0.7766609	0.3512825
600	0.3779	-1.8797	0.9966	A527	C763	0.7912866	-2.2489217	0.7766609	0.3341825
601	-0.7242	-0.7745	-0.3421	A376	C655	-0.2597926	-1.1730025	-0.5212327	0.3473475
602	-0.7114	2.9077	0.1140	A251	C123	-0.9422671	2.4806302	-0.5791599	0.4503656
603	0.9138	-0.4393	-0.1665	A601	C397	1.0336915	0.2140921	0.0921008	0.3439615
604	0.0627	-1.1320	0.4996	A462	C556	0.6025305	-0.9291853	0.3583787	0.2946222
605	0.9087	-0.7947	-0.6095	A623	C508	1.3298237	-0.7586967	-0.8086783	0.2187685
606	1.8464	-0.0336	0.9882	A763	C459	1.7910516	-0.5739146	0.9028013	0.2270206
607	-2.9173	-0.0762	0.3960	A16	C766	-2.7284759	-0.4976307	-0.3415241	0.4492596
608	0.7832	0.9168	-0.6076	A556	C287	0.5468719	1.0211322	-0.4670886	0.1603905
609	0.0917	1.1893	-0.5904	A473	C287	0.5468719	1.0211322	-0.4670886	0.2488837
610	-2.4844	-0.4466	0.8516	A74	C728	-1.9816416	-0.8223302	0.8717976	0.2995621
611	1.0797	0.9291	0.8178	A650	C228	0.8994003	1.2236527	0.8271905	0.1614143
612	2.9839	-0.3036	-0.0365	A887	C368	2.7225869	-0.3304495	-0.3889044	0.2135223
613	-0.9666	-0.2576	0.0269	A317	C536	-1.0323493	-0.1417128	0.3010375	0.1519246
614	2.6025	-0.0137	-0.7981	A842	C368	2.7225869	-0.3304495	-0.3889044	0.2820107
615	2.1026	-0.0162	-0.9947	A774	C175	1.9954496	0.9735682	-0.8296280	0.4206636
616	-0.3721	-0.9913	-0.3381	A410	C655	-0.2597926	-1.1730025	-0.5212327	0.1590475
617	-1.9990	-2.1315	-0.3868	A109	C873	-1.6544946	-2.1236132	0.5230898	0.4207607
618	0.9484	-2.8363	-0.1363	A787	C776	0.8378659	-2.2297098	-0.7821201	0.4543148
619	-0.8113	0.6863	-0.3484	A345	C342	-0.8373696	1.1920791	-0.7640059	0.3158182
620	0.4963	1.1174	-0.6290	A528	C287	0.5468719	1.0211322	-0.4670886	0.1029170
621	-1.6976	1.6626	0.9265	A115	C224	-1.4293520	1.9746821	0.7526839	0.2513821
622	-0.8346	0.6547	-0.3432	A345	C342	-0.8373696	1.1920791	-0.7640059	0.3203182
623	-1.9104	0.1590	0.9966	A140	C491	-2.1349643	0.6623576	0.8377438	0.2955927
624	1.6615	0.7008	-0.9805	A706	C175	1.9954496	0.9735682	-0.8296280	0.2525299
625	-1.1863	-0.1036	-0.5875	A266	C559	-1.4876296	-0.0265439	-0.7952792	0.1953883
626	-0.9353	0.3770	0.1297	A326	C536	-1.0323493	-0.1417128	0.3010375	0.2623665
627	-0.9250	0.6577	-0.5017	A320	C342	-0.8373696	1.1920791	-0.7640059	0.2947718
628	-1.5860	-1.6611	0.9550	A144	C873	-1.6544946	-2.1236132	0.5230898	0.3209727
629	-0.7780	-1.5671	-0.9681	A306	C802	-1.5935443	-1.4685237	-0.8727753	0.3364818
630	-1.4761	1.1025	0.9875	A184	C224	-1.4293520	1.9746821	0.7526839	0.3845821
631	2.9908	0.0053	0.1352	A885	C368	2.7225869	-0.3304495	-0.3889044	0.3760223
632	-0.7926	1.9329	-0.9960	A238	C342	-0.8373696	1.1920791	-0.7640059	0.3391949
633	-0.6700	-0.7761	0.2235	A362	C536	-1.0323493	-0.1417128	0.3010375	0.3580913
634	-0.0510	-1.2363	-0.6468	A487	C655	-0.2597926	-1.1730025	-0.5212327	0.1325525
635	2.6734	-1.2906	0.2485	A896	C676	2.1950559	-1.7495404	0.0972307	0.3628512
636	0.5278	1.1249	0.6529	A518	C228	0.8994003	1.2236527	0.8271905	0.2148812
637	2.2611	-1.8221	-0.4278	A890	C676	2.1950559	-1.7495404	0.0972307	0.2212115
638	0.9550	-2.5953	-0.6435	A772	C776	0.8378659	-2.2297098	-0.7821201	0.2071148
639	0.3332	-1.1295	0.5689	A504	C556	0.6025305	-0.9291853	0.3583787	0.2267222
640	-1.6869	1.3915	0.9824	A146	C224	-1.4293520	1.9746821	0.7526839	0.3568154
641	1.2814	-0.4910	-0.7784	A675	C508	1.3298237	-0.7586967	-0.8086783	0.1154662
642	1.3373	0.0711	-0.7505	A678	C508	1.3298237	-0.7586967	-0.8086783	0.2984838
643	-2.3426	-0.2812	0.9332	A106	C728	-1.9816416	-0.8223302	0.8717976	0.3211637
644	-2.0535	-0.5511	0.9920	A132	C728	-1.9816416	-0.8223302	0.8717976	0.1544304
645	1.5645	-0.9645	0.9868	A750	C459	1.7910516	-0.5739146	0.9028013	0.2337119
646	-1.1677	1.1147	0.9226	A257	C350	-0.5144181	1.0433207	0.4973778	0.3832945
647	-0.7142	-1.3197	0.8663	A348	C710	-0.4532110	-1.5200102	0.8113151	0.1720947
648	0.4973	1.3358	-0.8184	A545	C287	0.5468719	1.0211322	-0.4670886	0.2385170
649	-1.2766	-0.9069	-0.9009	A230	C802	-1.5935443	-1.4685237	-0.8727753	0.3022309
650	-0.1047	1.2116	0.6210	A433	C350	-0.5144181	1.0433207	0.4973778	0.2338732
651	0.5451	-0.9582	0.4409	A541	C556	0.6025305	-0.9291853	0.3583787	0.0563222
652	1.0237	-1.3468	0.9513	A686	C763	0.7912866	-2.2489217	0.7766609	0.4363914
653	-1.9703	1.8659	0.7006	A58	C224	-1.4293520	1.9746821	0.7526839	0.2339380
654	-1.9071	-1.2788	0.9551	A143	C728	-1.9816416	-0.8223302	0.8717976	0.2047712
655	-0.5663	-0.9971	0.5214	A374	C710	-0.4532110	-1.5200102	0.8113151	0.3086381
656	-1.1768	-1.7494	-0.9941	A244	C802	-1.5935443	-1.4685237	-0.8727753	0.2729818
657	0.9915	0.1298	-0.0034	A605	C397	1.0336915	0.2140921	0.0921008	0.0739948
658	1.1197	0.2369	0.5177	A638	C397	1.0336915	0.2140921	0.0921008	0.1781385
659	-2.4726	-0.4578	0.8574	A74	C728	-1.9816416	-0.8223302	0.8717976	0.2899621
660	-0.1487	1.0199	-0.2457	A425	C287	0.5468719	1.0211322	-0.4670886	0.3060642
661	-0.3825	-0.9778	0.3122	A412	C556	0.6025305	-0.9291853	0.3583787	0.3599413
662	-1.9952	2.0098	-0.5549	A73	C391	-2.3605439	1.3502882	-0.4417122	0.3793479
663	-1.0955	-0.8737	-0.8010	A276	C802	-1.5935443	-1.4685237	-0.8727753	0.3882144
664	-2.8689	-0.5962	0.3671	A17	C766	-2.7284759	-0.4976307	-0.3415241	0.3158725
665	-0.7615	-0.6614	0.1312	A362	C536	-1.0323493	-0.1417128	0.3010375	0.3201246
666	0.9510	2.8301	-0.1692	A689	C81	0.5783356	2.3154644	-0.7661384	0.4947461
667	1.5192	-0.3941	-0.9026	A718	C508	1.3298237	-0.7586967	-0.8086783	0.2159649
668	-1.8964	-1.4368	0.9253	A143	C728	-1.9816416	-0.8223302	0.8717976	0.2510712
669	0.8611	-0.5322	0.1564	A595	C556	0.6025305	-0.9291853	0.3583787	0.2858445
670	2.9715	0.0765	-0.2331	A885	C368	2.7225869	-0.3304495	-0.3889044	0.2705556
671	-0.2063	-1.6061	-0.9247	A476	C655	-0.2597926	-1.1730025	-0.5212327	0.2966858
672	-1.8075	2.1124	0.6255	A68	C224	-1.4293520	1.9746821	0.7526839	0.2143499
673	0.9326	-0.4126	-0.1979	A601	C397	1.0336915	0.2140921	0.0921008	0.3392615
674	-2.5497	-1.3456	0.4694	A41	C728	-1.9816416	-0.8223302	0.8717976	0.4979086
675	2.3383	-1.8533	0.1802	A897	C676	2.1950559	-1.7495404	0.0972307	0.1099910
676	2.7074	-0.6096	0.6317	A872	C459	1.7910516	-0.5739146	0.9028013	0.4077117
677	0.7332	-1.5833	0.9669	A656	C763	0.7912866	-2.2489217	0.7766609	0.3046492
678	-2.5141	1.5356	-0.3244	A26	C391	-2.3605439	1.3502882	-0.4417122	0.1520600
679	-0.7210	1.9651	0.9956	A338	C224	-1.4293520	1.9746821	0.7526839	0.3202834
680	-1.0511	0.1146	0.3337	A294	C536	-1.0323493	-0.1417128	0.3010375	0.1025754
681	-1.6382	-1.2696	-0.9974	A191	C802	-1.5935443	-1.4685237	-0.8727753	0.1227347
682	-1.9162	-1.1211	-0.9755	A145	C802	-1.5935443	-1.4685237	-0.8727753	0.2576013
683	-1.6278	-1.2954	-0.9968	A191	C802	-1.5935443	-1.4685237	-0.8727753	0.1104680
684	2.1898	-1.2694	-0.8473	A821	C508	1.3298237	-0.7586967	-0.8086783	0.4697671
685	0.6390	0.8862	-0.4202	A536	C287	0.5468719	1.0211322	-0.4670886	0.0913163
686	0.2255	-1.0178	0.2883	A506	C556	0.6025305	-0.9291853	0.3583787	0.1785747
687	0.8323	1.6587	0.9896	A572	C228	0.8994003	1.2236527	0.8271905	0.2215190
688	1.5240	2.3062	-0.6449	A752	C29	1.5896815	2.2890353	0.3101313	0.3459592
689	-1.9873	2.1806	0.3112	A32	C224	-1.4293520	1.9746821	0.7526839	0.4017833
690	0.8780	-1.7413	-0.9988	A707	C776	0.8378659	-2.2297098	-0.7821201	0.2484080
691	-1.0288	-1.9140	0.9849	A269	C710	-0.4532110	-1.5200102	0.8113151	0.3810546
692	2.7582	-1.0012	-0.3565	A895	C368	2.7225869	-0.3304495	-0.3889044	0.2462560
693	-1.2394	2.6797	0.3049	A137	C224	-1.4293520	1.9746821	0.7526839	0.4475846
694	-0.7087	-1.0217	-0.6539	A394	C655	-0.2597926	-1.1730025	-0.5212327	0.2442924
695	0.5694	-1.4943	0.9161	A598	C763	0.7912866	-2.2489217	0.7766609	0.3719825
696	0.2676	-2.7273	0.6722	A617	C763	0.7912866	-2.2489217	0.7766609	0.3688419
697	1.2457	2.4540	0.6591	A716	C29	1.5896815	2.2890353	0.3101313	0.2859716
698	-0.8476	1.6599	0.9907	A254	C224	-1.4293520	1.9746821	0.7526839	0.3781834
699	-2.7661	-0.9126	-0.4085	A33	C766	-2.7284759	-0.4976307	-0.3415241	0.1731898
700	2.6008	1.3228	0.3969	A858	C160	2.3972612	0.8131370	0.6512993	0.3225337
701	0.7697	-0.8689	0.5438	A584	C556	0.6025305	-0.9291853	0.3583787	0.1376253
702	0.5893	1.1522	-0.7084	A562	C287	0.5468719	1.0211322	-0.4670886	0.1382691
703	-0.5819	1.7348	0.9854	A332	C350	-0.5144181	1.0433207	0.4973778	0.4156611
704	0.1829	1.3122	0.7377	A461	C228	0.8994003	1.2236527	0.8271905	0.2981794
705	2.4055	-1.7710	0.1599	A897	C676	2.1950559	-1.7495404	0.0972307	0.0981910
706	1.6999	2.4717	-0.0212	A801	C29	1.5896815	2.2890353	0.3101313	0.2080715
707	0.3959	-1.6483	-0.9524	A555	C776	0.8378659	-2.2297098	-0.7821201	0.3978852
708	-1.9215	-1.9377	0.6846	A91	C873	-1.6544946	-2.1236132	0.5230898	0.2048096
709	-0.9732	2.7275	0.4442	A197	C123	-0.9422671	2.4806302	-0.5791599	0.4337209
710	1.5287	0.4109	0.9089	A685	C459	1.7910516	-0.5739146	0.9028013	0.4177550
711	1.0976	2.6824	0.4394	A700	C29	1.5896815	2.2890353	0.3101313	0.3382383
712	0.8678	0.5047	0.0878	A575	C397	1.0336915	0.2140921	0.0921008	0.1536001
713	-0.9541	-0.4217	0.2904	A316	C536	-1.0323493	-0.1417128	0.3010375	0.1229580
714	1.1273	-0.0050	0.4883	A624	C397	1.0336915	0.2140921	0.0921008	0.2362999
715	1.8537	-0.2190	-0.9911	A791	C508	1.3298237	-0.7586967	-0.8086783	0.4153315
716	-1.6331	0.9085	0.9914	A155	C491	-2.1349643	0.6623576	0.8377438	0.3005543
717	2.9290	0.6330	-0.0821	A871	C160	2.3972612	0.8131370	0.6512993	0.4817584
718	-2.4030	-0.7364	0.8582	A86	C728	-1.9816416	-0.8223302	0.8717976	0.1736288
719	1.4092	-0.3997	-0.8447	A701	C508	1.3298237	-0.7586967	-0.8086783	0.1581315
720	0.3504	1.0666	0.4800	A492	C350	-0.5144181	1.0433207	0.4973778	0.3018251
721	1.7803	-0.3913	-0.9842	A761	C508	1.3298237	-0.7586967	-0.8086783	0.3311315
722	0.5181	0.9235	0.3381	A514	C287	0.5468719	1.0211322	-0.4670886	0.3105309
723	-1.3025	1.7994	0.9752	A152	C224	-1.4293520	1.9746821	0.7526839	0.1748834
724	-0.0468	-1.3154	-0.7297	A480	C655	-0.2597926	-1.1730025	-0.5212327	0.1879525
725	1.8053	-1.1500	-0.9901	A784	C508	1.3298237	-0.7586967	-0.8086783	0.3494004
726	0.9214	1.7996	0.9998	A653	C228	0.8994003	1.2236527	0.8271905	0.2568521
727	2.8567	0.4996	0.4358	A875	C160	2.3972612	0.8131370	0.6512993	0.3294917
728	1.3966	0.3745	0.8325	A685	C397	1.0336915	0.2140921	0.0921008	0.4212385
729	0.7356	-0.7194	-0.2385	A560	C556	0.6025305	-0.9291853	0.3583787	0.3132445
730	1.4971	0.9398	0.9726	A696	C228	0.8994003	1.2236527	0.8271905	0.3423206
731	-0.6036	-2.7538	0.5735	A429	C881	-0.5693053	-2.7024202	-0.2819962	0.3137235
732	1.0188	-0.8862	-0.7602	A652	C508	1.3298237	-0.7586967	-0.8086783	0.1623351
733	2.9457	-0.5592	-0.0587	A891	C368	2.7225869	-0.3304495	-0.3889044	0.2606893
734	-1.3756	-1.2583	0.9907	A229	C728	-1.9816416	-0.8223302	0.8717976	0.3869712
735	2.5068	-1.2010	0.6263	A866	C676	2.1950559	-1.7495404	0.0972307	0.4631179
736	0.4084	2.4953	-0.8489	A526	C81	0.5783356	2.3154644	-0.7661384	0.1441776
737	-1.3132	-0.1509	-0.7350	A247	C559	-1.4876296	-0.0265439	-0.7952792	0.1196883
738	0.8587	-1.8953	0.9967	A705	C763	0.7912866	-2.2489217	0.7766609	0.2136914
739	-1.0051	-0.8628	0.7375	A285	C728	-1.9816416	-0.8223302	0.8717976	0.3837696
740	1.0835	-0.8138	-0.7642	A652	C508	1.3298237	-0.7586967	-0.8086783	0.1153018
741	-1.1953	-1.7418	-0.9937	A244	C802	-1.5935443	-1.4685237	-0.8727753	0.2641484
742	-1.2213	-0.0010	0.6274	A265	C536	-1.0323493	-0.1417128	0.3010375	0.2186754
743	-0.0005	2.0683	0.9977	A444	C100	-0.0270481	2.4238631	0.7389638	0.2136158
744	1.3984	-1.3943	-0.9997	A738	C508	1.3298237	-0.7586967	-0.8086783	0.2984004
745	1.8194	2.3066	0.3472	A801	C29	1.5896815	2.2890353	0.3101313	0.0947839
746	-0.9696	0.2533	-0.0662	A315	C536	-1.0323493	-0.1417128	0.3010375	0.2749999
747	-0.6299	0.7788	0.0579	A379	C350	-0.5144181	1.0433207	0.4973778	0.2731601
748	1.7060	-2.3834	0.3648	A860	C676	2.1950559	-1.7495404	0.0972307	0.4634949
749	1.5026	-0.6769	0.9360	A709	C459	1.7910516	-0.5739146	0.9028013	0.1415452
750	0.5832	-2.1223	0.9796	A609	C763	0.7912866	-2.2489217	0.7766609	0.1792158
751	0.7861	1.0137	0.6968	A570	C228	0.8994003	1.2236527	0.8271905	0.1512145
752	-1.9767	-1.3728	-0.9136	A124	C802	-1.5935443	-1.4685237	-0.8727753	0.1732347
753	-1.5887	-0.3799	-0.9304	A198	C559	-1.4876296	-0.0265439	-0.7952792	0.1965157
754	-0.6474	1.1225	0.7101	A361	C350	-0.5144181	1.0433207	0.4973778	0.1416278
755	2.9618	-0.0985	0.2681	A884	C368	2.7225869	-0.3304495	-0.3889044	0.3760556
756	0.1145	-1.5462	-0.8932	A476	C655	-0.2597926	-1.1730025	-0.5212327	0.3731525
757	1.3199	0.3591	0.7748	A648	C397	1.0336915	0.2140921	0.0921008	0.3713052
758	0.4148	0.9995	-0.3969	A509	C287	0.5468719	1.0211322	-0.4670886	0.0746309
759	-0.3169	-2.9822	0.0443	A471	C881	-0.5693053	-2.7024202	-0.2819962	0.2861604
760	-0.4887	1.8193	0.9932	A338	C350	-0.5144181	1.0433207	0.4973778	0.4325065
761	2.8001	-0.5224	-0.5294	A869	C368	2.7225869	-0.3304495	-0.3889044	0.1366531
762	2.8450	-0.8996	0.1792	A892	C368	2.7225869	-0.3304495	-0.3889044	0.4198893
763	1.0436	0.4599	-0.5111	A616	C397	1.0336915	0.2140921	0.0921008	0.2863058
764	0.5061	-1.1539	-0.6726	A542	C655	-0.2597926	-1.1730025	-0.5212327	0.3121208
765	-0.8963	0.7848	0.5883	A293	C350	-0.5144181	1.0433207	0.4973778	0.2437749
766	2.4513	-1.1179	-0.7198	A854	C368	2.7225869	-0.3304495	-0.3889044	0.4632110
767	1.7514	2.4179	0.1694	A801	C29	1.5896815	2.2890353	0.3101313	0.1437715
768	-0.3954	2.8410	-0.4960	A353	C123	-0.9422671	2.4806302	-0.5791599	0.3301323
769	0.4751	-2.1536	-0.9787	A667	C776	0.8378659	-2.2297098	-0.7821201	0.2118186
770	-2.0393	-1.2246	-0.9255	A124	C802	-1.5935443	-1.4685237	-0.8727753	0.2474680
771	2.4005	-0.0915	-0.9155	A815	C368	2.7225869	-0.3304495	-0.3889044	0.3625440
772	-2.3548	-0.9765	0.8357	A86	C728	-1.9816416	-0.8223302	0.8717976	0.1878086
773	1.2128	2.5475	0.5703	A700	C29	1.5896815	2.2890353	0.3101313	0.2985050
774	0.5125	0.8649	-0.1029	A532	C287	0.5468719	1.0211322	-0.4670886	0.1849309
775	-1.4884	-0.3639	-0.8839	A236	C559	-1.4876296	-0.0265439	-0.7952792	0.1422491
776	1.2618	1.2080	0.9674	A683	C228	0.8994003	1.2236527	0.8271905	0.1727540
777	2.4297	1.2723	0.6697	A829	C160	2.3972612	0.8131370	0.6512993	0.1700008
778	-0.3028	1.6778	0.9555	A387	C100	-0.0270481	2.4238631	0.7389638	0.4127837
779	-2.1889	-1.3746	-0.8112	A124	C802	-1.5935443	-1.4685237	-0.8727753	0.2502849
780	-2.1308	1.9345	-0.4788	A36	C391	-2.3605439	1.3502882	-0.4417122	0.2836812
781	1.1060	0.2686	-0.5072	A633	C397	1.0336915	0.2140921	0.0921008	0.2420391
782	-2.0614	0.4863	-0.9930	A148	C559	-1.4876296	-0.0265439	-0.7952792	0.4281117
783	-2.1095	-0.7776	-0.9687	A151	C802	-1.5935443	-1.4685237	-0.8727753	0.4342680
784	1.0880	0.4100	0.5466	A619	C397	1.0336915	0.2140921	0.0921008	0.2349052
785	-2.8250	-0.1845	0.5562	A16	C766	-2.7284759	-0.4976307	-0.3415241	0.4357929
786	-1.3837	2.1356	-0.8387	A179	C123	-0.9422671	2.4806302	-0.5791599	0.3486677
787	-1.9571	-2.2288	0.2581	A76	C873	-1.6544946	-2.1236132	0.5230898	0.2242607
788	-0.1386	2.3071	-0.9503	A450	C81	0.5783356	2.3154644	-0.7661384	0.3031539
789	1.9489	1.6841	-0.8177	A764	C175	1.9954496	0.9735682	-0.8296280	0.2563364
790	1.2229	-1.5158	0.9986	A730	C763	0.7912866	-2.2489217	0.7766609	0.4622247
791	-1.2651	1.0873	-0.9433	A242	C342	-0.8373696	1.1920791	-0.7640059	0.2372679
792	1.3984	2.5134	0.4820	A766	C29	1.5896815	2.2890353	0.3101313	0.1958383
793	0.4248	-2.9574	0.1560	A666	C881	-0.5693053	-2.7024202	-0.2819962	0.5623604
794	-0.6322	-0.7750	-0.0190	A393	C655	-0.2597926	-1.1730025	-0.5212327	0.4242142
795	-2.5513	-0.1628	-0.8308	A87	C766	-2.7284759	-0.4976307	-0.3415241	0.3337608
796	-1.4412	-2.5578	0.3522	A157	C873	-1.6544946	-2.1236132	0.5230898	0.2727904
797	2.7424	-1.1609	-0.2087	A895	C368	2.7225869	-0.3304495	-0.3889044	0.3434893
798	0.8014	-0.6374	-0.2178	A599	C556	0.6025305	-0.9291853	0.3583787	0.3556112
799	1.2973	-1.7640	-0.9818	A780	C776	0.8378659	-2.2297098	-0.7821201	0.3749413
800	1.0011	0.2249	0.2269	A606	C397	1.0336915	0.2140921	0.0921008	0.0593995
801	0.7159	-0.8662	0.4819	A584	C556	0.6025305	-0.9291853	0.3583787	0.0999587
802	0.8922	-0.5875	0.3630	A600	C556	0.6025305	-0.9291853	0.3583787	0.2119920
803	-1.9785	-0.0361	-0.9998	A139	C559	-1.4876296	-0.0265439	-0.7952792	0.2349824
804	-1.3674	2.1201	-0.8524	A179	C123	-0.9422671	2.4806302	-0.5791599	0.3529677
805	-0.9486	0.4066	-0.2511	A321	C536	-1.0323493	-0.1417128	0.3010375	0.3947332
806	1.2211	-2.0825	-0.9102	A740	C776	0.8378659	-2.2297098	-0.7821201	0.2195080
807	0.5222	2.2603	0.9475	A547	C100	-0.0270481	2.4238631	0.7389638	0.3071158
808	2.7256	1.2202	-0.1652	A859	C160	2.3972612	0.8131370	0.6512993	0.5173003
809	-1.3923	-1.2367	-0.9905	A208	C802	-1.5935443	-1.4685237	-0.8727753	0.1835976
810	-1.0875	-1.0794	0.8839	A252	C710	-0.4532110	-1.5200102	0.8113151	0.3824947
811	-2.3473	1.6903	-0.4510	A26	C391	-2.3605439	1.3502882	-0.4417122	0.1208479
812	1.8120	-2.3875	0.0744	A863	B3	1.7531600	-2.4276200	-0.0842200	0.0858600
813	2.4761	-1.6027	-0.3137	A898	C676	2.1950559	-1.7495404	0.0972307	0.2796051
814	1.3049	1.7304	-0.9859	A726	C81	0.5783356	2.3154644	-0.7661384	0.5104635
815	-1.5047	1.4938	-0.9927	A167	C342	-0.8373696	1.1920791	-0.7640059	0.3992485
816	1.6961	-1.2147	-0.9963	A784	C508	1.3298237	-0.7586967	-0.8086783	0.3366338
817	-0.9778	-1.6698	0.9979	A253	C710	-0.4532110	-1.5200102	0.8113151	0.2869879
818	-2.7921	0.2335	0.5975	A14	C491	-2.1349643	0.6623576	0.8377438	0.4420790
819	-1.6231	1.4452	-0.9849	A167	C342	-0.8373696	1.1920791	-0.7640059	0.4199152
820	-1.7918	-1.7586	-0.8598	A149	C802	-1.5935443	-1.4685237	-0.8727753	0.1671024
821	-1.3379	2.6052	0.3710	A121	C224	-1.4293520	1.9746821	0.7526839	0.3678846
822	-1.3311	-0.4546	-0.8049	A236	C559	-1.4876296	-0.0265439	-0.7952792	0.1980688
823	2.5796	0.8393	0.7014	A829	C160	2.3972612	0.8131370	0.6512993	0.0862008
824	1.0925	-0.5470	0.6280	A644	C459	1.7910516	-0.5739146	0.9028013	0.3334225
825	0.0623	1.5983	0.9163	A439	C100	-0.0270481	2.4238631	0.7389638	0.3640825
826	-2.8267	0.7702	-0.3682	A25	C391	-2.3605439	1.3502882	-0.4417122	0.3732521
827	1.2564	1.9053	0.9593	A694	C228	0.8994003	1.2236527	0.8271905	0.3902521
828	1.1981	2.2696	-0.8241	A729	C81	0.5783356	2.3154644	-0.7661384	0.2411968
829	-1.7416	1.4897	0.9565	A146	C224	-1.4293520	1.9746821	0.7526839	0.3336821
830	1.0336	-0.2709	-0.3639	A625	C397	1.0336915	0.2140921	0.0921008	0.3136948
831	0.4195	2.2638	-0.9532	A526	C81	0.5783356	2.3154644	-0.7661384	0.1325205
832	1.2244	0.8993	0.8768	A650	C228	0.8994003	1.2236527	0.8271905	0.2329873
833	-0.1695	0.9855	-0.0037	A426	C350	-0.5144181	1.0433207	0.4973778	0.3012722
834	-2.1325	1.0724	0.9221	A118	C491	-2.1349643	0.6623576	0.8377438	0.1656210
835	0.9996	0.1172	-0.1138	A605	C397	1.0336915	0.2140921	0.0921008	0.1122948
836	-2.3292	1.0997	0.8176	A71	C491	-2.1349643	0.6623576	0.8377438	0.2172406
837	0.0351	-1.1239	0.4830	A462	C556	0.6025305	-0.9291853	0.3583787	0.2955888
838	0.2351	2.8032	0.5822	A440	C100	-0.0270481	2.4238631	0.7389638	0.2660830
839	2.3001	0.9930	0.8629	A804	C160	2.3972612	0.8131370	0.6512993	0.1628750
840	-1.5402	-1.8112	0.9260	A194	C873	-1.6544946	-2.1236132	0.5230898	0.2765393
841	-1.5858	-2.0236	0.8210	A147	C873	-1.6544946	-2.1236132	0.5230898	0.1555393
842	0.0052	1.5450	-0.8905	A442	C342	-0.8373696	1.1920791	-0.7640059	0.4406615
843	0.3211	1.6671	0.9532	A513	C228	0.8994003	1.2236527	0.8271905	0.3825857
844	2.1852	0.5381	0.9681	A793	C160	2.3972612	0.8131370	0.6512993	0.2679663
845	2.8491	-0.8149	-0.2684	A888	C368	2.7225869	-0.3304495	-0.3889044	0.2438227
846	-0.3646	1.8874	-0.9970	A382	C342	-0.8373696	1.1920791	-0.7640059	0.4670282
847	0.5713	2.3279	0.9178	A547	C100	-0.0270481	2.4238631	0.7389638	0.2910491
848	0.4314	-1.2739	0.7556	A553	C556	0.6025305	-0.9291853	0.3583787	0.3043555
849	-0.4816	0.9482	0.3506	A378	C350	-0.5144181	1.0433207	0.4973778	0.0915722
850	-0.2094	-1.2389	-0.6687	A452	C655	-0.2597926	-1.1730025	-0.5212327	0.0879191
851	-0.3845	1.1105	0.5653	A392	C350	-0.5144181	1.0433207	0.4973778	0.0883399
852	-0.4227	-2.8208	0.5231	A429	C881	-0.5693053	-2.7024202	-0.2819962	0.3566938
853	2.2319	-1.8207	-0.4744	A873	C676	2.1950559	-1.7495404	0.0972307	0.2265448
854	0.7735	-0.8837	0.5642	A584	C556	0.6025305	-0.9291853	0.3583787	0.1407587
855	-0.8531	-1.4457	0.9470	A280	C710	-0.4532110	-1.5200102	0.8113151	0.2032947
856	-2.1654	0.1173	-0.9857	A139	C559	-1.4876296	-0.0265439	-0.7952792	0.3373450
857	-0.4133	0.9233	0.1519	A398	C350	-0.5144181	1.0433207	0.4973778	0.1888722
858	0.3064	-0.9570	0.0988	A525	C556	0.6025305	-0.9291853	0.3583787	0.1945080
859	0.4397	-1.3233	-0.7958	A535	C655	-0.2597926	-1.1730025	-0.5212327	0.3747858
860	0.6082	-2.9195	0.1879	A731	C763	0.7912866	-2.2489217	0.7766609	0.4808086
861	-1.9010	-0.3327	0.9975	A150	C728	-1.9816416	-0.8223302	0.8717976	0.2319914
862	-1.1718	2.2755	-0.8288	A219	C123	-0.9422671	2.4806302	-0.5791599	0.2281011
863	2.7476	0.7469	0.5312	A851	C160	2.3972612	0.8131370	0.6512993	0.1788917
864	-2.5761	-0.9133	-0.6800	A70	C766	-2.7284759	-0.4976307	-0.3415241	0.3021737
865	0.0124	-2.9452	-0.3265	A516	C881	-0.5693053	-2.7024202	-0.2819962	0.2896630
866	0.9754	-0.5410	0.4664	A628	C556	0.6025305	-0.9291853	0.3583787	0.2896920
867	-0.9695	-0.5161	-0.4323	A335	C536	-1.0323493	-0.1417128	0.3010375	0.3901913
868	-0.1966	-1.3076	-0.7354	A455	C655	-0.2597926	-1.1730025	-0.5212327	0.1373191
869	1.4617	-0.5118	0.8924	A697	C459	1.7910516	-0.5739146	0.9028013	0.1339558
870	-1.1555	-0.1048	0.5429	A271	C536	-1.0323493	-0.1417128	0.3010375	0.1339754
871	1.5318	-1.3975	-0.9973	A738	C508	1.3298237	-0.7586967	-0.8086783	0.3431338
872	-1.9226	-1.9712	0.6573	A91	C873	-1.6544946	-2.1236132	0.5230898	0.1849096
873	-1.9403	1.8255	0.7477	A117	C224	-1.4293520	1.9746821	0.7526839	0.2217046
874	-0.6796	1.2470	0.8147	A336	C350	-0.5144181	1.0433207	0.4973778	0.2287278
875	-0.1613	1.0129	-0.2252	A425	C287	0.5468719	1.0211322	-0.4670886	0.3194309
876	-0.6133	1.5167	-0.9314	A357	C342	-0.8373696	1.1920791	-0.7640059	0.2386949
877	-2.6175	-1.3702	-0.2983	A23	C766	-2.7284759	-0.4976307	-0.3415241	0.3422564
878	0.4819	-2.0337	0.9959	A609	C763	0.7912866	-2.2489217	0.7766609	0.2479492
879	-1.1432	-0.4086	-0.6183	A267	C559	-1.4876296	-0.0265439	-0.7952792	0.3011550
880	-1.0775	-1.2856	0.9465	A298	C710	-0.4532110	-1.5200102	0.8113151	0.3312947
881	-0.2063	1.2247	-0.6522	A432	C342	-0.8373696	1.1920791	-0.7640059	0.2584988
882	-0.3126	1.9148	0.9982	A405	C100	-0.0270481	2.4238631	0.7389638	0.3512837
883	1.9226	-2.2090	-0.3714	A864	C676	2.1950559	-1.7495404	0.0972307	0.4001821
884	0.2436	-1.6665	-0.9488	A555	C776	0.8378659	-2.2297098	-0.7821201	0.4413852
885	-2.5837	1.4946	0.1736	A6	C391	-2.3605439	1.3502882	-0.4417122	0.3275934
886	0.5240	-2.3070	-0.9307	A688	C776	0.8378659	-2.2297098	-0.7821201	0.1799120
887	-0.6504	0.7928	-0.2241	A371	C350	-0.5144181	1.0433207	0.4973778	0.3693268
888	0.7531	-1.0172	-0.6788	A610	C508	1.3298237	-0.7586967	-0.8086783	0.3217018
889	-0.7239	2.6588	-0.6550	A287	C123	-0.9422671	2.4806302	-0.5791599	0.1574590
890	0.0674	2.3913	-0.9199	A450	C81	0.5783356	2.3154644	-0.7661384	0.2468443
891	-1.5652	0.3799	-0.9211	A215	C559	-1.4876296	-0.0265439	-0.7952792	0.2032783
892	0.4389	-1.3194	-0.7928	A535	C655	-0.2597926	-1.1730025	-0.5212327	0.3722191
893	0.3523	-2.9723	0.1176	A666	C881	-0.5693053	-2.7024202	-0.2819962	0.5303604
894	-2.7257	-0.9674	0.4515	A30	C766	-2.7284759	-0.4976307	-0.3415241	0.4218564
895	-0.7362	2.8026	-0.4406	A250	C123	-0.9422671	2.4806302	-0.5791599	0.2221989
896	0.4608	0.9515	-0.3334	A509	C287	0.5468719	1.0211322	-0.4670886	0.0964642
897	-0.9475	-0.3572	-0.1585	A330	C536	-1.0323493	-0.1417128	0.3010375	0.2532913
898	0.8691	0.5017	-0.0834	A578	C397	1.0336915	0.2140921	0.0921008	0.2092334
899	-1.3751	0.1097	0.7841	A227	C536	-1.0323493	-0.1417128	0.3010375	0.3590754
900	-1.8520	-0.8448	-0.9994	A151	C802	-1.5935443	-1.4685237	-0.8727753	0.3362680
901	-1.6301	0.3771	-0.9451	A182	C559	-1.4876296	-0.0265439	-0.7952792	0.2319783
902	-1.0574	-1.1416	-0.8960	A318	C802	-1.5935443	-1.4685237	-0.8727753	0.2954309
903	-1.0258	-0.5064	-0.5169	A305	C536	-1.0323493	-0.1417128	0.3010375	0.3963913
904	0.7855	2.2340	0.9298	A627	C100	-0.0270481	2.4238631	0.7389638	0.3977491
905	-0.1088	-1.6831	-0.9496	A475	C655	-0.2597926	-1.1730025	-0.5212327	0.3631525
906	-0.4492	2.2182	0.9647	A363	C100	-0.0270481	2.4238631	0.7389638	0.2845170
907	0.4590	1.7579	-0.9831	A530	C81	0.5783356	2.3154644	-0.7661384	0.2979539
908	-0.4843	0.8750	-0.0129	A389	C350	-0.5144181	1.0433207	0.4973778	0.2362389
909	-1.2724	0.5443	0.7877	A258	C491	-2.1349643	0.6623576	0.8377438	0.3435552
910	-0.8224	-2.7464	-0.4986	A245	C881	-0.5693053	-2.7024202	-0.2819962	0.1712261
911	2.7113	-0.7916	0.5659	A886	C368	2.7225869	-0.3304495	-0.3889044	0.4757473
912	1.3150	-1.5734	0.9987	A730	C763	0.7912866	-2.2489217	0.7766609	0.4737581
913	-0.0896	-2.1376	0.9902	A507	C710	-0.4532110	-1.5200102	0.8113151	0.3866953
914	0.2347	1.5590	0.9059	A495	C228	0.8994003	1.2236527	0.8271905	0.3595857
915	-2.3118	-1.2366	-0.7832	A89	C802	-1.5935443	-1.4685237	-0.8727753	0.3465849
916	2.4548	-0.8983	-0.7894	A846	C368	2.7225869	-0.3304495	-0.3889044	0.4120444
917	-1.5621	-0.8875	-0.9791	A187	C802	-1.5935443	-1.4685237	-0.8727753	0.2395976
918	0.7140	-0.7037	-0.0701	A573	C556	0.6025305	-0.9291853	0.3583787	0.2551445
919	0.3019	-1.7019	0.9624	A527	C710	-0.4532110	-1.5200102	0.8113151	0.3626953
920	-0.4251	2.3952	0.9016	A281	C100	-0.0270481	2.4238631	0.7389638	0.1964504
921	2.3704	0.3195	-0.9200	A805	C175	1.9954496	0.9735682	-0.8296280	0.3731302
922	-2.4501	-0.5077	0.8648	A56	C728	-1.9816416	-0.8223302	0.8717976	0.2633621
923	-2.6727	1.3550	-0.0830	A9	C391	-2.3605439	1.3502882	-0.4417122	0.2251934
924	-1.9432	-0.4913	1.0000	A156	C728	-1.9816416	-0.8223302	0.8717976	0.1658914
925	-1.4864	1.9480	0.8929	A152	C224	-1.4293520	1.9746821	0.7526839	0.0746487
926	-0.1271	-2.7524	0.6553	A486	C881	-0.5693053	-2.7024202	-0.2819962	0.4764938
927	0.6923	-2.6805	-0.6399	A733	C776	0.8378659	-2.2297098	-0.7821201	0.2461920
928	-0.0360	2.5596	0.8286	A434	C100	-0.0270481	2.4238631	0.7389638	0.0781083
929	2.1069	-1.5891	0.7692	A824	C676	2.1950559	-1.7495404	0.0972307	0.3068552
930	2.5221	-1.1986	-0.6100	A854	C368	2.7225869	-0.3304495	-0.3889044	0.4299110
931	-0.9856	0.3668	0.3172	A304	C536	-1.0323493	-0.1417128	0.3010375	0.1904749
932	0.7638	2.8281	-0.3690	A569	C81	0.5783356	2.3154644	-0.7661384	0.3650795
933	-0.7350	-0.8900	0.5336	A374	C710	-0.4532110	-1.5200102	0.8113151	0.3965047
934	2.9613	0.3816	0.1681	A875	C160	2.3972612	0.8131370	0.6512993	0.4929250
935	1.1394	-2.7751	0.0131	A823	B4	1.3630182	-2.6647182	-0.0442455	0.1304485
936	2.9177	0.0183	-0.3970	A876	C368	2.7225869	-0.3304495	-0.3889044	0.1839861
937	1.2673	0.1687	0.6924	A659	C397	1.0336915	0.2140921	0.0921008	0.2930999
938	0.9708	2.5691	0.6655	A700	C100	-0.0270481	2.4238631	0.7389638	0.4055163
939	0.4998	0.8990	-0.2373	A519	C287	0.5468719	1.0211322	-0.4670886	0.1329976
940	-0.5049	0.8725	-0.1269	A389	C350	-0.5144181	1.0433207	0.4973778	0.2682055
941	0.5969	0.9729	-0.5127	A531	C287	0.5468719	1.0211322	-0.4670886	0.0479572
942	-2.6983	-1.2378	0.2484	A30	C766	-2.7284759	-0.4976307	-0.3415241	0.4534231
943	0.8018	1.1506	-0.8018	A585	C287	0.5468719	1.0211322	-0.4670886	0.2397024
944	2.3511	0.6178	-0.9024	A817	C175	1.9954496	0.9735682	-0.8296280	0.2613969
945	-0.8167	0.6568	-0.3061	A345	C342	-0.8373696	1.1920791	-0.7640059	0.3379515
946	-2.4149	-1.7734	0.0877	A52	B7	-2.3318600	-1.8725200	0.1143200	0.0695933
947	1.7972	-1.3389	-0.9705	A784	C508	1.3298237	-0.7586967	-0.8086783	0.4031338
948	-0.6392	-2.8255	-0.4422	A384	C881	-0.5693053	-2.7024202	-0.2819962	0.1177261
949	1.3753	-0.4742	-0.8383	A692	C508	1.3298237	-0.7586967	-0.8086783	0.1198649
950	-0.9870	0.4045	0.3591	A304	C536	-1.0323493	-0.1417128	0.3010375	0.2165415
951	2.4998	-0.3782	0.8491	A830	C459	1.7910516	-0.5739146	0.9028013	0.3193881
952	1.4232	-2.0919	-0.8479	A807	C776	0.8378659	-2.2297098	-0.7821201	0.2629746
953	0.2677	1.0791	0.4596	A492	C350	-0.5144181	1.0433207	0.4973778	0.2852251
954	1.2752	-1.1133	-0.9516	A703	C508	1.3298237	-0.7586967	-0.8086783	0.1840496
955	-0.9509	-1.1166	-0.8459	A342	C802	-1.5935443	-1.4685237	-0.8727753	0.3404811
956	-1.0314	-0.1408	-0.2833	A309	C536	-1.0323493	-0.1417128	0.3010375	0.1953999
957	-0.9190	1.8937	0.9945	A254	C224	-1.4293520	1.9746821	0.7526839	0.2777167
958	1.7216	0.3399	-0.9695	A732	C175	1.9954496	0.9735682	-0.8296280	0.3491299
959	0.7969	0.7094	-0.3597	A557	C287	0.5468719	1.0211322	-0.4670886	0.2230496
960	-0.9273	2.7901	0.3408	A192	C123	-0.9422671	2.4806302	-0.5791599	0.4147989
961	2.0903	0.3563	0.9927	A776	C160	2.3972612	0.8131370	0.6512993	0.3683997
962	2.0831	2.1314	0.1974	A836	C29	1.5896815	2.2890353	0.3101313	0.2545950
963	-0.2232	2.4002	0.9119	A363	C100	-0.0270481	2.4238631	0.7389638	0.1309170
964	1.5952	-2.3964	-0.4772	A847	C776	0.8378659	-2.2297098	-0.7821201	0.4096481
965	-1.0195	1.7248	1.0000	A233	C224	-1.4293520	1.9746821	0.7526839	0.3023501
966	2.6734	0.1140	-0.7371	A838	C368	2.7225869	-0.3304495	-0.3889044	0.2806107
967	1.7650	-1.6558	0.9075	A796	C459	1.7910516	-0.5739146	0.9028013	0.3708786
968	0.8482	-0.6181	-0.3108	A599	C508	1.3298237	-0.7586967	-0.8086783	0.3733662
969	0.0026	-1.0002	-0.0210	A474	C655	-0.2597926	-1.1730025	-0.5212327	0.3118092
970	1.0801	-0.2942	0.4739	A639	C397	1.0336915	0.2140921	0.0921008	0.3121666
971	-0.0106	2.5606	-0.8281	A400	C81	0.5783356	2.3154644	-0.7661384	0.2986776
972	0.8477	1.6050	0.9827	A572	C228	0.8994003	1.2236527	0.8271905	0.1961857
973	0.3534	-1.6079	0.9354	A539	C710	-0.4532110	-1.5200102	0.8113151	0.3395286
974	0.4017	1.1145	-0.5790	A501	C287	0.5468719	1.0211322	-0.4670886	0.1168170
975	1.3725	-0.7583	-0.9019	A713	C508	1.3298237	-0.7586967	-0.8086783	0.0454315
976	-0.0271	0.9997	0.0067	A449	C350	-0.5144181	1.0433207	0.4973778	0.3405389
977	-0.9028	-0.4593	0.1600	A350	C536	-1.0323493	-0.1417128	0.3010375	0.1960580
978	-0.5592	2.9106	0.2664	A251	C100	-0.0270481	2.4238631	0.7389638	0.4971509
979	-0.9973	-2.4039	-0.7981	A232	C881	-0.5693053	-2.7024202	-0.2819962	0.4142062
980	0.3857	2.0988	0.9910	A547	C100	-0.0270481	2.4238631	0.7389638	0.3299491
981	-2.3473	0.7687	-0.8827	A92	C391	-2.3605439	1.3502882	-0.4417122	0.3452733
982	0.5050	1.1216	-0.6381	A528	C287	0.5468719	1.0211322	-0.4670886	0.1044504
983	-0.7064	-0.8184	-0.3946	A376	C655	-0.2597926	-1.1730025	-0.5212327	0.3092809
984	2.0318	-0.7054	0.9886	A779	C459	1.7910516	-0.5739146	0.9028013	0.1526775
985	-1.1852	1.2823	-0.9672	A237	C342	-0.8373696	1.1920791	-0.7640059	0.2137485
986	-1.4971	0.2476	-0.8759	A228	C559	-1.4876296	-0.0265439	-0.7952792	0.1214117
987	-0.8561	-0.6772	-0.4180	A335	C655	-0.2597926	-1.1730025	-0.5212327	0.3984475
988	-0.8928	-0.4866	0.1827	A350	C536	-1.0323493	-0.1417128	0.3010375	0.2009246
989	-0.3445	2.0960	-0.9923	A365	C81	0.5783356	2.3154644	-0.7661384	0.4561539
990	-2.9348	-0.2855	-0.3164	A5	C766	-2.7284759	-0.4976307	-0.3415241	0.1478596
991	-2.7377	-0.2260	0.6648	A45	C766	-2.7284759	-0.4976307	-0.3415241	0.4290596
992	0.7107	2.5872	-0.7304	A618	C81	0.5783356	2.3154644	-0.7661384	0.1466128
993	-1.0415	-0.2291	0.3582	A290	C536	-1.0323493	-0.1417128	0.3010375	0.0512335
994	-1.0222	-2.4375	0.7657	A210	C873	-1.6544946	-2.1236132	0.5230898	0.3962639
995	2.8401	0.8724	0.2388	A852	C160	2.3972612	0.8131370	0.6512993	0.3048670
996	0.5626	0.8335	-0.1057	A532	C287	0.5468719	1.0211322	-0.4670886	0.1882496
997	-1.5951	0.0871	-0.9154	A212	C559	-1.4876296	-0.0265439	-0.7952792	0.1137450
998	0.8443	-2.0716	-0.9715	A676	C776	0.8378659	-2.2297098	-0.7821201	0.1179746
999	2.2937	0.8478	0.8954	A804	C160	2.3972612	0.8131370	0.6512993	0.1274416
1000	1.4904	-0.4691	0.8992	A697	C459	1.7910516	-0.5739146	0.9028013	0.1363558


hist(act_pred$diff, breaks = 30, col = "blue", main = "Mean Absolute Difference", xlab = "Difference")

Figure 22: Mean Absolute Difference

HVT Scoring Cells with Layers using scoreLayeredHVT

Zubin Dowlaty, Srinivasan Sudarsanam, Somya Shambhawi

2024-02-12

1. Abstract

2. Example : HVT with the Torus dataset

3. Map A : Base Compressed Map

4. Map B : Compressed Novelty Map

4.1 Voronoi Tessellation with highlighted novelty cell

5. Map C : Compressed Map without Novelty

5.1 Iteration 1:

5.2 Iteration 2:

6. Scoring on Test Data

7. Executive Summary

8. References